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ComplexListPlot
plots complex numbers z1, z2, … as points in the complex plane.
plots with features defined by the symbolic wrapper w.
Details and Options




- The datai have the following forms and interpretations:
-
<"k1"z1,"k2"z2,… > values {z1,z2,…} {z1"lbl1",z2"lbl2",…}, {z1,z2,…}{"lbl1","lbl2",…} values {z1,z2,…} with labels {lbl1,lbl2,…} SparseArray values as a normal array - ComplexListPlot[Tabular[…]cspec] extracts and plots values from the tabular object using the column specification cspec.
- The following forms of column specifications cspec are allowed for plotting tabular data:
-
col plot complex values from column col {col1,col2,…} plot values from columns col1, col2, … - The following wrappers w can be used for the datai:
-
Annotation[datai,label] provide an annotation for the data Button[datai,action] define an action to execute when the data is clicked Callout[datai,label] label the data with a callout Callout[datai,label,pos] place the callout at relative position pos EventHandler[datai,…] define a general event handler for the data Highlighted[datai,effect] dynamically highlight fi with an effect Highlighted[datai,Placed[effect,pos]] statically highlight fi with an effect at position pos Hyperlink[datai,uri] make the data a hyperlink Labeled[datai,label] label the data Labeled[datai,label,pos] place the label at relative position pos Legended[datai,label] identify the data in a legend PopupWindow[datai,cont] attach a popup window to the data StatusArea[datai,label] display in the status area on mouseover Style[datai,styles] show the data using the specified styles Tooltip[datai,label] attach a tooltip to the data Tooltip[datai] use data values as tooltips - Wrappers w can be applied at multiple levels:
-
{…,w[zi],…} wrap the value zi in data w[datai] wrap the data w[{data1,…}] wrap a collection of datai w1[w2[…]] use nested wrappers - Callout, Labeled and Placed can use the following positions pos:
-
Automatic automatically placed labels Above, Below, Before, After positions around the data x near the data at a position x Scaled[s] scaled position s along the data {s,Above},{s,Below},… relative position at position s along the data {pos,epos} epos in label placed at relative position pos of the data - ComplexListPlot has the same options as Graphics, with the following additions and changes: [List of all options]
-
Axes True whether to draw axes Joined False whether to join points LabelingFunction Automatic how to label points LabelingSize Automatic maximum size of callouts and labels PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotHighlighting Automatic highlighting effect for curves PlotLabel None overall label for the plot PlotLabels None labels for data PlotLegends None legends for data PlotMarkers None markers to use to indicate each point PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to determine styles of points PlotTheme $PlotTheme overall theme for the plot PolarAxes False whether to draw polar axes PolarAxesOrigin Automatic where to draw polar axes PolarGridLines None polar gridlines to draw PolarTicks Automatic polar axes ticks ScalingFunctions None how to scale individual coordinates - LabelingFunction->f specifies that each point should have a label given by f[value,index,lbls], where value is the value associated with the point, index is its position in the data and lbls is the list of relevant labels.
- Typical settings for PlotLegends include:
-
None no legend Automatic automatically determine legend {lbl1,lbl2,…} use lbl1, lbl2, … as legend labels Placed[lspec,…] specify placement for legend - The arguments supplied to functions in MeshFunctionsare x, y, θ, r where θ and r are the argument and radius of the zi. Functions in ColorFunction are by default supplied with scaled versions of these arguments.
- Possible highlighting effects for Highlighted and PlotHighlighting include:
-
style highlight the indicated data "Ball" highlight and label the indicated point in data "Dropline" highlight and label the indicated point in data with droplines to the axes "XSlice" highlight and label all points along a vertical slice "YSlice" highlight and label all points along a horizontal slice Placed[effect,pos] statically highlight the given position pos - Highlight position specifications pos include:
-
x, {x} effect at {x,y}, with y chosen automatically {x,y} effect at {x,y} {pos1,pos2,…} multiple positions posi - ScalingFunctions->"scale" scales the modulus of the zi. ScalingFunctions{"scalex","scaley"} scales the
and imaginary components, respectively.
-
AlignmentPoint Center the default point in the graphic to align with AspectRatio Automatic ratio of height to width Axes True whether to draw axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} style specifications for the axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic ContentSelectable Automatic whether to allow contents to be selected CoordinatesToolOptions Automatic detailed behavior of the coordinates tool Epilog {} primitives rendered after the main plot FormatType TraditionalForm the default format type for text Frame False whether to put a frame around the plot FrameLabel None frame labels FrameStyle {} style specifications for the frame FrameTicks Automatic frame ticks FrameTicksStyle {} style specifications for frame ticks GridLines None grid lines to draw GridLinesStyle {} style specifications for grid lines ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels etc. ImageSize Automatic the absolute size at which to render the graphic Joined False whether to join points LabelingFunction Automatic how to label points LabelingSize Automatic maximum size of callouts and labels LabelStyle {} style specifications for labels Method Automatic details of graphics methods to use PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotHighlighting Automatic highlighting effect for curves PlotLabel None overall label for the plot PlotLabels None labels for data PlotLegends None legends for data PlotMarkers None markers to use to indicate each point PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic the final display region to be filled PlotStyle Automatic graphics directives to determine styles of points PlotTheme $PlotTheme overall theme for the plot PolarAxes False whether to draw polar axes PolarAxesOrigin Automatic where to draw polar axes PolarGridLines None polar gridlines to draw PolarTicks Automatic polar axes ticks PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} primitives rendered before the main plot RotateLabel True whether to rotate y labels on the frame ScalingFunctions None how to scale individual coordinates Ticks Automatic axes ticks TicksStyle {} style specifications for axes ticks
List of all options




Examples
open allclose allBasic Examples (4)Summary of the most common use cases
Plot a set of complex numbers:

https://wolfram.com/xid/0b0kdli4gyq-fa9rpt

Plot multiple sets of complex numbers:

https://wolfram.com/xid/0b0kdli4gyq-y4lg0


https://wolfram.com/xid/0b0kdli4gyq-f5cb96

Label each point with a callout:

https://wolfram.com/xid/0b0kdli4gyq-bhb9ep

Scope (39)Survey of the scope of standard use cases
Data (7)
A list of complex values is plotted as a list of
pairs:

https://wolfram.com/xid/0b0kdli4gyq-onptp

Plot multiple sets of regular data:

https://wolfram.com/xid/0b0kdli4gyq-ndwvlt

Non-numeric and missing data is excluded:

https://wolfram.com/xid/0b0kdli4gyq-12pt6

Use MaxPlotPoints to limit the number of points used:

https://wolfram.com/xid/0b0kdli4gyq-bv6ei3

PlotRange is selected automatically:

https://wolfram.com/xid/0b0kdli4gyq-idhawk

Use PlotRange to focus on areas of interest:

https://wolfram.com/xid/0b0kdli4gyq-co2fga

Use ScalingFunctions to scale the axes:

https://wolfram.com/xid/0b0kdli4gyq-jg7wx0

Tabular Data (1)
Get tabular data of the results of running Newton's method to solve with random starting seeds:

https://wolfram.com/xid/0b0kdli4gyq-ciejmj

Plot all the points in the table:

https://wolfram.com/xid/0b0kdli4gyq-jxngsy

Use PivotToColumns to generate columns for each basin of attraction:

https://wolfram.com/xid/0b0kdli4gyq-5vtci

Plot each number per region separately:

https://wolfram.com/xid/0b0kdli4gyq-sv25t

Special Data (4)
Specify strings to use as labels:

https://wolfram.com/xid/0b0kdli4gyq-e4kgd6


Specify a location for labels:

https://wolfram.com/xid/0b0kdli4gyq-bzc2s6

Numeric values in an Association are used as the coordinates:

https://wolfram.com/xid/0b0kdli4gyq-gv8lu

Plot data in a SparseArray:

https://wolfram.com/xid/0b0kdli4gyq-he2wo1

Wrappers (6)
Use wrappers on individual data, datasets or collections of datasets:

https://wolfram.com/xid/0b0kdli4gyq-cfxi2w


https://wolfram.com/xid/0b0kdli4gyq-dzdsjn

Use a specific label for all of the points:

https://wolfram.com/xid/0b0kdli4gyq-iorflv

Label points with automatically positioned text:

https://wolfram.com/xid/0b0kdli4gyq-kr574s

Use PopupWindow to click an eigenvalue to see a corresponding eigenvector:

https://wolfram.com/xid/0b0kdli4gyq-da4zmv

Button can be used to trigger any action:

https://wolfram.com/xid/0b0kdli4gyq-b5m17y

Labeling and Legending (15)
Label points with automatically positioned text:

https://wolfram.com/xid/0b0kdli4gyq-bq6s41

Place the labels relative to the points:

https://wolfram.com/xid/0b0kdli4gyq-1fdhh

Label data with Labeled:

https://wolfram.com/xid/0b0kdli4gyq-2ypsg

Label data with PlotLabels:

https://wolfram.com/xid/0b0kdli4gyq-f52kdd

Place the label near the points at a particular value:

https://wolfram.com/xid/0b0kdli4gyq-qa5qq


https://wolfram.com/xid/0b0kdli4gyq-gsqoel

Specify the text position relative to the point:

https://wolfram.com/xid/0b0kdli4gyq-joao2v

Label data automatically with Callout:

https://wolfram.com/xid/0b0kdli4gyq-eie4u

Place a label with a specific location:

https://wolfram.com/xid/0b0kdli4gyq-dej9qj

Specify label names with LabelingFunction:

https://wolfram.com/xid/0b0kdli4gyq-enusz0


https://wolfram.com/xid/0b0kdli4gyq-m91ju4

For dense sets of points, some labels may be turned into tooltips by default:

https://wolfram.com/xid/0b0kdli4gyq-dltqyp

Increasing the size of the plot will show more labels:

https://wolfram.com/xid/0b0kdli4gyq-xnc4v

Include legends for each datai:

https://wolfram.com/xid/0b0kdli4gyq-oecqe7

Use Legended to provide a legend for a specific dataset:

https://wolfram.com/xid/0b0kdli4gyq-ctpkwm

Use Placed to change the legend location:

https://wolfram.com/xid/0b0kdli4gyq-bdwmi

Use association keys as labels:

https://wolfram.com/xid/0b0kdli4gyq-ce3uya

Plots usually have interactive callouts showing the coordinates when you mouse over them:

https://wolfram.com/xid/0b0kdli4gyq-wniqin

Presentation (6)
Multiple datasets are automatically colored to be distinct:

https://wolfram.com/xid/0b0kdli4gyq-cre3xb

Provide explicit styling to different sets:

https://wolfram.com/xid/0b0kdli4gyq-ffzx0b


https://wolfram.com/xid/0b0kdli4gyq-ra4kf

Include legends for each dataset:

https://wolfram.com/xid/0b0kdli4gyq-f7c0ah

Use Legended to provide a legend for a specific dataset:

https://wolfram.com/xid/0b0kdli4gyq-g1ojsp

Provide an interactive Tooltip for the data:

https://wolfram.com/xid/0b0kdli4gyq-dg3ihr

Use shapes to distinguish different datasets:

https://wolfram.com/xid/0b0kdli4gyq-ec792w

Use labels to distinguish different datasets:

https://wolfram.com/xid/0b0kdli4gyq-t94vk

Use Joined to connect datasets with lines:

https://wolfram.com/xid/0b0kdli4gyq-hfamz7

Use InterpolationOrder to smooth joined data:

https://wolfram.com/xid/0b0kdli4gyq-fd948k

Options (156)Common values & functionality for each option
AspectRatio (4)
By default, the ratio of the height to width for the plot is determined automatically:

https://wolfram.com/xid/0b0kdli4gyq-c780x0

Use numerical value to specify the height to width ratio:

https://wolfram.com/xid/0b0kdli4gyq-t49nh

Make the height the same as the width with AspectRatio1:

https://wolfram.com/xid/0b0kdli4gyq-c2kdfa

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

https://wolfram.com/xid/0b0kdli4gyq-bphtkg

Axes (3)
By default, ComplexListPlot draws axes:

https://wolfram.com/xid/0b0kdli4gyq-b4nyf4

Use AxesOrigin to specify where the axes intersect:

https://wolfram.com/xid/0b0kdli4gyq-baiju6

Turn each axis on individually:

https://wolfram.com/xid/0b0kdli4gyq-hrvnif

AxesLabel (3)
No axes labels are drawn by default:

https://wolfram.com/xid/0b0kdli4gyq-bmcqp5


https://wolfram.com/xid/0b0kdli4gyq-dcp604


https://wolfram.com/xid/0b0kdli4gyq-eotbup

AxesOrigin (2)
The position of the axes is determined automatically:

https://wolfram.com/xid/0b0kdli4gyq-bs480

Specify an explicit origin for the axes:

https://wolfram.com/xid/0b0kdli4gyq-cyatyl

AxesStyle (4)
Change the style for the axes:

https://wolfram.com/xid/0b0kdli4gyq-fdcaf

Specify the style of each axis:

https://wolfram.com/xid/0b0kdli4gyq-njwgf

Use different styles for the ticks and the axes:

https://wolfram.com/xid/0b0kdli4gyq-jw6j7w

Use different styles for the labels and the axes:

https://wolfram.com/xid/0b0kdli4gyq-gkpgwo

ClippingStyle (4)
ClippingStyle requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-g25ymh

Omit clipped regions of the plot:

https://wolfram.com/xid/0b0kdli4gyq-ge6v6

Show clipped regions as red at the bottom and thick at the top:

https://wolfram.com/xid/0b0kdli4gyq-s338x

Show clipped regions as red and thick:

https://wolfram.com/xid/0b0kdli4gyq-muuui0

ColorFunction (3)
Color by scaled ,
,
and
coordinates:

https://wolfram.com/xid/0b0kdli4gyq-b4mxcp

ColorFunction has higher priority than PlotStyle for coloring the curve:

https://wolfram.com/xid/0b0kdli4gyq-hqd8e3

Use Automatic in MeshShading to use ColorFunction:

https://wolfram.com/xid/0b0kdli4gyq-eo0aq2

ColorFunctionScaling (4)
ColorFunctionScaling requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-b7gv9b

Color the curve based on the scaled value:

https://wolfram.com/xid/0b0kdli4gyq-i3p4mr

Color the curve based on the unscaled value:

https://wolfram.com/xid/0b0kdli4gyq-x4myc

Color by unscaled ,
,
and
coordinates:

https://wolfram.com/xid/0b0kdli4gyq-cdmsuu

Frame (3)

https://wolfram.com/xid/0b0kdli4gyq-2uekv9

Draw a frame on the left and right edges:

https://wolfram.com/xid/0b0kdli4gyq-cgev1a

Draw a frame on the left and bottom edges:

https://wolfram.com/xid/0b0kdli4gyq-z9e9k8

FrameLabel (4)
Place a label along the bottom edge of the frame:

https://wolfram.com/xid/0b0kdli4gyq-117ns0

Place labels on the bottom and left edges:

https://wolfram.com/xid/0b0kdli4gyq-mikz4k

Place labels on each of the edges in the frame:

https://wolfram.com/xid/0b0kdli4gyq-orwd79

Use a customized style for both labels and frame tick labels:

https://wolfram.com/xid/0b0kdli4gyq-3p7ebj

FrameStyle (2)
FrameTicks (9)
Frame ticks are placed automatically by default:

https://wolfram.com/xid/0b0kdli4gyq-vjujys


https://wolfram.com/xid/0b0kdli4gyq-enmj35

Use frame ticks on the bottom edge:

https://wolfram.com/xid/0b0kdli4gyq-svax9j

By default, the top and right edges have tick marks but no tick labels:

https://wolfram.com/xid/0b0kdli4gyq-r0k90y

Use All to include tick labels on all edges:

https://wolfram.com/xid/0b0kdli4gyq-uxa1lq

Place tick marks at specific positions:

https://wolfram.com/xid/0b0kdli4gyq-uotnoy

Draw frame tick marks at specified positions with specific labels:

https://wolfram.com/xid/0b0kdli4gyq-shjlxi

Specify the lengths for tick marks as a fraction of the graphics size:

https://wolfram.com/xid/0b0kdli4gyq-d4o29s

Use different sizes in the positive and negative directions for each tick mark:

https://wolfram.com/xid/0b0kdli4gyq-lvj5db

Specify a style for each frame tick:

https://wolfram.com/xid/0b0kdli4gyq-gfebzc

Construct a function that places frame ticks at the midpoint and extremes of the frame edge:

https://wolfram.com/xid/0b0kdli4gyq-vi9cv3

https://wolfram.com/xid/0b0kdli4gyq-uoqwba

FrameTicksStyle (3)
By default, frame ticks and frame tick labels use the same styles as the frame:

https://wolfram.com/xid/0b0kdli4gyq-u7c3jz

Specify an overall style for the ticks, including the labels:

https://wolfram.com/xid/0b0kdli4gyq-e44wux

Use different styles for the different frame edges:

https://wolfram.com/xid/0b0kdli4gyq-7rwp05

ImageSize (8)
Use named sizes such as Tiny, Small, Medium and Large:

https://wolfram.com/xid/0b0kdli4gyq-b481gq

Specify the width of the plot:

https://wolfram.com/xid/0b0kdli4gyq-hm4sz5

Specify the height of the plot:

https://wolfram.com/xid/0b0kdli4gyq-g1fk47

Allow the width and height to be up to a certain size:

https://wolfram.com/xid/0b0kdli4gyq-b9tvo5

Specify the width and height for a graphic, padding with space if necessary:

https://wolfram.com/xid/0b0kdli4gyq-ci7gw

Setting AspectRatioFull will fill the available space:

https://wolfram.com/xid/0b0kdli4gyq-liooi1

Use maximum sizes for the width and height:

https://wolfram.com/xid/0b0kdli4gyq-crsz5o

Use ImageSizeFull to fill the available space in an object:

https://wolfram.com/xid/0b0kdli4gyq-cm9co2

Specify the image size as a fraction of the available space:

https://wolfram.com/xid/0b0kdli4gyq-bbyr2i

The number of points that are labeled directly may depend on the image size:

https://wolfram.com/xid/0b0kdli4gyq-jbo2y1

https://wolfram.com/xid/0b0kdli4gyq-cjcsee

Smaller graphics will have fewer labeled points:

https://wolfram.com/xid/0b0kdli4gyq-6g3sr

Larger graphics will have more labeled points:

https://wolfram.com/xid/0b0kdli4gyq-ckt10t

InterpolationOrder (4)
InterpolationOrder requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-bwwbis

By default, linear interpolation is used:

https://wolfram.com/xid/0b0kdli4gyq-b1qz4l

Use zero-order or piecewise-constant interpolation:

https://wolfram.com/xid/0b0kdli4gyq-gvzhio


https://wolfram.com/xid/0b0kdli4gyq-o14yfg

Joined (3)

https://wolfram.com/xid/0b0kdli4gyq-ddykp1

Join the first dataset with a line, but use points for the second dataset:

https://wolfram.com/xid/0b0kdli4gyq-fb2qpr

Join the dataset with a line and show the original points:

https://wolfram.com/xid/0b0kdli4gyq-b74azt

LabelingFunction (7)
A Rule can be used to label points if the lists of values and labels are the same length:

https://wolfram.com/xid/0b0kdli4gyq-et8sm

A list of rules and values can be used to label selected points:

https://wolfram.com/xid/0b0kdli4gyq-edtrib

Use LabelingFunctionNone to suppress the labels:

https://wolfram.com/xid/0b0kdli4gyq-br9yle

Put the labels above the points:

https://wolfram.com/xid/0b0kdli4gyq-im4ibf

Put them in a Tooltip:

https://wolfram.com/xid/0b0kdli4gyq-iioey2

Label the points as ordered pairs:

https://wolfram.com/xid/0b0kdli4gyq-bk9m50

Label the points with their indices:

https://wolfram.com/xid/0b0kdli4gyq-gipuqx

LabelingSize (3)
Textual labels are shown at their actual sizes:

https://wolfram.com/xid/0b0kdli4gyq-ftj27o

Specify a maximum size for textual labels:

https://wolfram.com/xid/0b0kdli4gyq-g4u8up

Image labels are automatically resized:

https://wolfram.com/xid/0b0kdli4gyq-cl4r9b

https://wolfram.com/xid/0b0kdli4gyq-hrz1j

Specify a maximum size for image labels:

https://wolfram.com/xid/0b0kdli4gyq-i8twek

Show image labels at their natural sizes:

https://wolfram.com/xid/0b0kdli4gyq-ch3lws

MaxPlotPoints (1)
Use MaxPlotPoints to limit the number of points used:

https://wolfram.com/xid/0b0kdli4gyq-nb1ke

Mesh (6)
Mesh requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-fndgu2

The initial and final sampling meshes are typically the same:

https://wolfram.com/xid/0b0kdli4gyq-fsofqf

Interpolated data may introduce points:

https://wolfram.com/xid/0b0kdli4gyq-pwtt0

Use 20 mesh levels evenly spaced in the direction:

https://wolfram.com/xid/0b0kdli4gyq-bys3w8

Use an explicit list of values for the mesh in the direction:

https://wolfram.com/xid/0b0kdli4gyq-d3z8sl

Use explicit styles at specific points:

https://wolfram.com/xid/0b0kdli4gyq-h5xkr8

MeshFunctions (3)
MeshFunctions requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-bubjpu

Show 5 mesh levels in the direction (red) and 10 in the
direction (blue):

https://wolfram.com/xid/0b0kdli4gyq-bi65fy

Use a mesh evenly spaced in the ,
,
and
directions:

https://wolfram.com/xid/0b0kdli4gyq-fesfzl

MeshShading (7)
MeshShading requires at least one dataset to be Joined:

https://wolfram.com/xid/0b0kdli4gyq-gmohjd

Alternate red and blue segments of equal width in the direction:

https://wolfram.com/xid/0b0kdli4gyq-imab9u

Use None to remove segments:

https://wolfram.com/xid/0b0kdli4gyq-ei3p0h

MeshShading can be used with PlotStyle:

https://wolfram.com/xid/0b0kdli4gyq-b705by

MeshShading has higher priority than PlotStyle:

https://wolfram.com/xid/0b0kdli4gyq-ko6bm1

Use PlotStyle for some segments by setting MeshShading to Automatic:

https://wolfram.com/xid/0b0kdli4gyq-e4hq1

MeshShading can be used with ColorFunction:

https://wolfram.com/xid/0b0kdli4gyq-mkb2zd

PlotHighlighting (7)
Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

https://wolfram.com/xid/0b0kdli4gyq-biyxlf

Use PlotHighlightingNone to disable the highlighting for the entire plot:

https://wolfram.com/xid/0b0kdli4gyq-gi3xrl

Use Highlighted[…,None] to disable highlighting for a single set:

https://wolfram.com/xid/0b0kdli4gyq-gx1xdf

Move the mouse over a set of points to highlight it using arbitrary graphics directives:

https://wolfram.com/xid/0b0kdli4gyq-d38t9z

Move the mouse over the points to highlight them with balls and labels:

https://wolfram.com/xid/0b0kdli4gyq-ca8a5x

Move the mouse over the curve to highlight it with a label and droplines to the axes:

https://wolfram.com/xid/0b0kdli4gyq-bq0orm

Use a component that shows the points on the plot closest to the position of the mouse cursor:

https://wolfram.com/xid/0b0kdli4gyq-cu66ho

Specify the style for the points:

https://wolfram.com/xid/0b0kdli4gyq-h6qclv

Use a component that shows the coordinates on the points closest to the mouse cursor:

https://wolfram.com/xid/0b0kdli4gyq-rrp8p

Use Callout options to change the appearance of the label:

https://wolfram.com/xid/0b0kdli4gyq-kh4jnq

Combine components to create a custom effect:

https://wolfram.com/xid/0b0kdli4gyq-ttn3g

PlotLabel (1)
PlotLabels (5)
Specify text to label sets of points:

https://wolfram.com/xid/0b0kdli4gyq-kyulg0

Place the labels above the points:

https://wolfram.com/xid/0b0kdli4gyq-bnlq2k

Use callouts to identify the points:

https://wolfram.com/xid/0b0kdli4gyq-i8gmt8

Use the keys from an Association as labels:

https://wolfram.com/xid/0b0kdli4gyq-bl1kwh

Use None to not add a label:

https://wolfram.com/xid/0b0kdli4gyq-j8n6u

PlotLegends (6)
Generate a legend using labels:

https://wolfram.com/xid/0b0kdli4gyq-mc3e3

Generate a legend using placeholders:

https://wolfram.com/xid/0b0kdli4gyq-bo6rg0

Legends use the same styles as the plot:

https://wolfram.com/xid/0b0kdli4gyq-bs6y4z

Use Placed to specify the legend placement:

https://wolfram.com/xid/0b0kdli4gyq-hqzurg

Place the legend inside the plot:

https://wolfram.com/xid/0b0kdli4gyq-cepi9e

Use PlotLegends to change the appearance:

https://wolfram.com/xid/0b0kdli4gyq-f3ejr9

PlotMarkers (8)
ComplexListPlot normally uses distinct colors to distinguish different sets of data:

https://wolfram.com/xid/0b0kdli4gyq-o95qz

Automatically use colors and shapes to distinguish sets of data:

https://wolfram.com/xid/0b0kdli4gyq-q0wtn


https://wolfram.com/xid/0b0kdli4gyq-cqebpi

Change the size of the default plot markers:

https://wolfram.com/xid/0b0kdli4gyq-h3fs16

Use arbitrary text for plot markers:

https://wolfram.com/xid/0b0kdli4gyq-cza700

Use explicit graphics for plot markers:

https://wolfram.com/xid/0b0kdli4gyq-gawwlz


https://wolfram.com/xid/0b0kdli4gyq-dh9jee

Use the same symbol for all the sets of data:

https://wolfram.com/xid/0b0kdli4gyq-eoo6qr

Explicitly use a symbol and size:

https://wolfram.com/xid/0b0kdli4gyq-bp54rs

PlotRange (4)
PlotRange is automatically calculated:

https://wolfram.com/xid/0b0kdli4gyq-fdwqx4


https://wolfram.com/xid/0b0kdli4gyq-86akp

Explicitly choose the and
ranges:

https://wolfram.com/xid/0b0kdli4gyq-etrmn3

Implicitly choose the and
ranges by giving complex coordinates of the bottom-left and top-right corners:

https://wolfram.com/xid/0b0kdli4gyq-dvcv2

PlotStyle (7)
Use different style directives:

https://wolfram.com/xid/0b0kdli4gyq-bllhzo

By default, different styles are chosen for multiple datasets:

https://wolfram.com/xid/0b0kdli4gyq-l8vxzn

Explicitly specify the style for different datasets:

https://wolfram.com/xid/0b0kdli4gyq-f0zft

PlotStyle applies to both curves and points:

https://wolfram.com/xid/0b0kdli4gyq-thtcd

PlotStyle can be combined with ColorFunction:

https://wolfram.com/xid/0b0kdli4gyq-fdc3g6

PlotStyle can be combined with MeshShading:

https://wolfram.com/xid/0b0kdli4gyq-bzc0v1

MeshStyle by default uses the same style as PlotStyle:

https://wolfram.com/xid/0b0kdli4gyq-fyjan

PlotTheme (2)
PolarAxes (2)
PolarAxesOrigin (2)
Specify the angular axes and radial axes to intersect at :

https://wolfram.com/xid/0b0kdli4gyq-cjbsgs

Place radial axes at the right of the graph:

https://wolfram.com/xid/0b0kdli4gyq-eptakz

PolarGridLines (2)
Use automatically chosen polar grid lines:

https://wolfram.com/xid/0b0kdli4gyq-h1a3pi

Draw grid lines at the specified positions:

https://wolfram.com/xid/0b0kdli4gyq-lheix


https://wolfram.com/xid/0b0kdli4gyq-fa8hfj

PolarTicks (4)
Place polar tick marks and labels automatically:

https://wolfram.com/xid/0b0kdli4gyq-ba7fbb


https://wolfram.com/xid/0b0kdli4gyq-h8wa7e


https://wolfram.com/xid/0b0kdli4gyq-vhhat

Place polar tick marks at the specified positions:

https://wolfram.com/xid/0b0kdli4gyq-drdk8q

ScalingFunctions (3)
A single scaling function scales the data radially:

https://wolfram.com/xid/0b0kdli4gyq-c5ain6


https://wolfram.com/xid/0b0kdli4gyq-exq5ll

Specifying two scaling functions scales the data in the and
directions separately:

https://wolfram.com/xid/0b0kdli4gyq-cwttv6

None indicates no scaling in the specified direction:

https://wolfram.com/xid/0b0kdli4gyq-cirsir

Ticks (9)
Ticks are placed automatically for each axis:

https://wolfram.com/xid/0b0kdli4gyq-lju0za

Use TicksNone to draw axes without any tick marks:

https://wolfram.com/xid/0b0kdli4gyq-4rcikc

Use ticks on the axis, but not the imaginary axis:

https://wolfram.com/xid/0b0kdli4gyq-jjj5zt

Place tick marks at specific positions:

https://wolfram.com/xid/0b0kdli4gyq-phvevx

Draw tick marks at the specified positions with specific labels:

https://wolfram.com/xid/0b0kdli4gyq-yv4x4o

Use specific ticks on one axis and automatic ticks on the other:

https://wolfram.com/xid/0b0kdli4gyq-4vca9p

Specify the lengths for ticks as a fraction of graphics size:

https://wolfram.com/xid/0b0kdli4gyq-it14fx

Use different sizes in the positive and negative directions for each tick:

https://wolfram.com/xid/0b0kdli4gyq-yg0h6d

Specify a style for each tick:

https://wolfram.com/xid/0b0kdli4gyq-uexqrq

Construct a function that places ticks at the midpoint and extremes of the axis:

https://wolfram.com/xid/0b0kdli4gyq-xdn9kh

https://wolfram.com/xid/0b0kdli4gyq-8686t5

TicksStyle (4)
By default, the ticks and tick labels use the same styles as the axis:

https://wolfram.com/xid/0b0kdli4gyq-658u1k

Specify an overall ticks style, including the tick labels:

https://wolfram.com/xid/0b0kdli4gyq-tmlpka

Specify ticks style for each of the axes:

https://wolfram.com/xid/0b0kdli4gyq-igvxm

Use a different style for the tick labels and tick marks:

https://wolfram.com/xid/0b0kdli4gyq-b45chz

Applications (9)Sample problems that can be solved with this function

https://wolfram.com/xid/0b0kdli4gyq-mvpsoi

Plot a discrete time signal and its spectrum:

https://wolfram.com/xid/0b0kdli4gyq-c0gvrq

https://wolfram.com/xid/0b0kdli4gyq-ml02o2

Graph zeros of the zeta function:

https://wolfram.com/xid/0b0kdli4gyq-o3me3

Graph eigenvalues of a Cauchy matrix:

https://wolfram.com/xid/0b0kdli4gyq-e7t3yx

https://wolfram.com/xid/0b0kdli4gyq-u1asv


https://wolfram.com/xid/0b0kdli4gyq-e3dmjr

https://wolfram.com/xid/0b0kdli4gyq-b1u3fq

Show Gershgorin discs and eigenvalues for a matrix:

https://wolfram.com/xid/0b0kdli4gyq-gbsop2

https://wolfram.com/xid/0b0kdli4gyq-eyvkz0

Show the eigenvalues for a PDE problem. Seek solutions of the structurally damped wave equation ,
of the form
:

https://wolfram.com/xid/0b0kdli4gyq-flasqv

Visualize iterations of Newton's method:

https://wolfram.com/xid/0b0kdli4gyq-ecy6jc

The eigenvalues of bipartite graphs are symmetric about the imaginary axis:

https://wolfram.com/xid/0b0kdli4gyq-j1he8c

https://wolfram.com/xid/0b0kdli4gyq-bqyhok

Properties & Relations (9)Properties of the function, and connections to other functions
Use ListPlot, ListLinePlot or ListPolarPlot for real data:

https://wolfram.com/xid/0b0kdli4gyq-b2uhcv

ComplexListPlot is closely related to ListPlot:

https://wolfram.com/xid/0b0kdli4gyq-bi09de

Use ComplexPlot to use color to show the argument and magnitude of a function:

https://wolfram.com/xid/0b0kdli4gyq-e28611

Use ComplexPlot3D to use the axis for the magnitude:

https://wolfram.com/xid/0b0kdli4gyq-vgce1e

Use ComplexArrayPlot for arrays of complex numbers:

https://wolfram.com/xid/0b0kdli4gyq-p6xumo

Use ReImPlot and AbsArgPlot to plot complex values over the real numbers:

https://wolfram.com/xid/0b0kdli4gyq-0vi62l


https://wolfram.com/xid/0b0kdli4gyq-mqa938

ComplexContourPlot plots curves over the complexes:

https://wolfram.com/xid/0b0kdli4gyq-pesif0

ComplexRegionPlot plots regions over the complexes:

https://wolfram.com/xid/0b0kdli4gyq-ko83ut

ComplexStreamPlot and ComplexVectorPlot treat complex numbers as directions:

https://wolfram.com/xid/0b0kdli4gyq-1lc4cy


https://wolfram.com/xid/0b0kdli4gyq-7studa

Possible Issues (2)Common pitfalls and unexpected behavior
Real-valued data is plotted along the axis.:

https://wolfram.com/xid/0b0kdli4gyq-dlw8r

Radial scaling is different when using the same scaling functions in the real and imaginary directions:

https://wolfram.com/xid/0b0kdli4gyq-pxhxjs

Neat Examples (3)Surprising or curious use cases
Eigenvalue analysis of the weighted adjacency matrix of the wins by teams in the National Hockey League in the 2010–2011 regular season:

https://wolfram.com/xid/0b0kdli4gyq-qkg6


Symmetry in the real parts of the eigenvalues of an adjacency matrix for a graph suggests that the graph may be bipartite, but in this case the graph is not bipartite:

https://wolfram.com/xid/0b0kdli4gyq-kjbssb



Compute an integer two times the numbers in {0,1,…,n-1} modulo :

https://wolfram.com/xid/0b0kdli4gyq-cyodma

Graphically represent the integer as the point
in the complex plane and connect the dots between the points representing
and
:

https://wolfram.com/xid/0b0kdli4gyq-d3fpe1

If you use a larger value of , then an envelope appears:

https://wolfram.com/xid/0b0kdli4gyq-dstk5g

Use multiples of three and five instead:

https://wolfram.com/xid/0b0kdli4gyq-4u6k2y


https://wolfram.com/xid/0b0kdli4gyq-v9dygh

Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2025).
Text
Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2025).
Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2025).
CMS
Wolfram Language. 2019. "ComplexListPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ComplexListPlot.html.
Wolfram Language. 2019. "ComplexListPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/ComplexListPlot.html.
APA
Wolfram Language. (2019). ComplexListPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexListPlot.html
Wolfram Language. (2019). ComplexListPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexListPlot.html
BibTeX
@misc{reference.wolfram_2025_complexlistplot, author="Wolfram Research", title="{ComplexListPlot}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexListPlot.html}", note=[Accessed: 23-March-2025
]}
BibLaTeX
@online{reference.wolfram_2025_complexlistplot, organization={Wolfram Research}, title={ComplexListPlot}, year={2025}, url={https://reference.wolfram.com/language/ref/ComplexListPlot.html}, note=[Accessed: 23-March-2025
]}