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ComplexListPlot[{z1,z2,}]

plots complex numbers z1, z2, as points in the complex plane.

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ComplexListPlot[{data1,data2,}]

plots data from all datai.

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ComplexListPlot[{,w[datai,],}]

plots data_(i) with features defined by the symbolic wrapper w.

Details and Options

Examples

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Basic Examples  (4)Summary of the most common use cases

Plot a set of complex numbers:

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Plot multiple sets of complex numbers:

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Plot several data_i with a legend:

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Label each point with a callout:

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Scope  (38)Survey of the scope of standard use cases

Data  (7)

A list of complex values is plotted as a list of {Re[z_(i)],Im[z_(i)]} pairs:

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Plot multiple sets of regular data:

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Non-numeric and missing data is excluded:

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Use MaxPlotPoints to limit the number of points used:

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PlotRange is selected automatically:

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Use PlotRange to focus on areas of interest:

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Use ScalingFunctions to scale the axes:

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Special Data  (4)

Specify strings to use as labels:

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Specify a location for labels:

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Numeric values in an Association are used as the (x,y) coordinates:

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Plot data in a SparseArray:

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Wrappers  (6)

Use wrappers on individual data, datasets or collections of datasets:

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Wrappers can be nested:

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Use a specific label for all of the points:

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Label points with automatically positioned text:

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

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Button can be used to trigger any action:

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Labeling and Legending  (15)

Label points with automatically positioned text:

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Place the labels relative to the points:

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Label data with Labeled:

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Label data with PlotLabels:

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Place the label near the points at a particular x value:

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Use a scaled position:

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Specify the text position relative to the point:

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Label data automatically with Callout:

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Place a label with a specific location:

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Specify label names with LabelingFunction:

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

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Increasing the size of the plot will show more labels:

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Include legends for each datai:

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Use Legended to provide a legend for a specific dataset:

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Use Placed to change the legend location:

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Use association keys as labels:

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

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Presentation  (6)

Multiple datasets are automatically colored to be distinct:

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Provide explicit styling to different sets:

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Use a plot theme:

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Include legends for each dataset:

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Use Legended to provide a legend for a specific dataset:

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Provide an interactive Tooltip for the data:

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Use shapes to distinguish different datasets:

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Use labels to distinguish different datasets:

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Use Joined to connect datasets with lines:

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Use InterpolationOrder to smooth joined data:

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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:

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Use numerical value to specify the height to width ratio:

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Make the height the same as the width with AspectRatio1:

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

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Axes  (3)

By default, ComplexListPlot draws axes:

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Use AxesOrigin to specify where the axes intersect:

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Turn each axis on individually:

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AxesLabel  (3)

No axes labels are drawn by default:

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Place a label on the axis:

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Specify axes labels:

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AxesOrigin  (2)

The position of the axes is determined automatically:

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Specify an explicit origin for the axes:

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AxesStyle  (4)

Change the style for the axes:

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Specify the style of each axis:

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Use different styles for the ticks and the axes:

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Use different styles for the labels and the axes:

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ClippingStyle  (4)

ClippingStyle requires at least one dataset to be Joined:

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Omit clipped regions of the plot:

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

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Show clipped regions as red and thick:

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ColorFunction  (3)

Color by scaled x, y, theta and r coordinates:

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ColorFunction has higher priority than PlotStyle for coloring the curve:

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Use Automatic in MeshShading to use ColorFunction:

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ColorFunctionScaling  (4)

ColorFunctionScaling requires at least one dataset to be Joined:

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Color the curve based on the scaled y value:

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Color the curve based on the unscaled y value:

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Color by unscaled x, y, theta and r coordinates:

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Frame  (3)

Draw a frame around the plot:

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Draw a frame on the left and right edges:

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Draw a frame on the left and bottom edges:

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FrameLabel  (4)

Place a label along the bottom edge of the frame:

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Place labels on the bottom and left edges:

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Place labels on each of the edges in the frame:

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

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FrameStyle  (2)

Specify a style for the frame:

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Specify a style for each frame edge:

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FrameTicks  (9)

Frame ticks are placed automatically by default:

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Use a frame with no ticks:

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Use frame ticks on the bottom edge:

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

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Use All to include tick labels on all edges:

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Place tick marks at specific positions:

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Draw frame tick marks at specified positions with specific labels:

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

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

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Specify a style for each frame tick:

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

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FrameTicksStyle  (3)

By default, frame ticks and frame tick labels use the same styles as the frame:

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

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Use different styles for the different frame edges:

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ImageSize  (8)

Use named sizes such as Tiny, Small, Medium and Large:

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Specify the width of the plot:

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Specify the height of the plot:

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

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

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Setting AspectRatioFull will fill the available space:

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Use maximum sizes for the width and height:

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Use ImageSizeFull to fill the available space in an object:

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

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

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Smaller graphics will have fewer labeled points:

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Larger graphics will have more labeled points:

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InterpolationOrder  (4)

InterpolationOrder requires at least one dataset to be Joined:

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By default, linear interpolation is used:

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Use zero-order or piecewise-constant interpolation:

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Interpolation order 0 to 3:

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Joined  (3)

Join the points in a dataset:

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

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

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LabelingFunction  (7)

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

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

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Use LabelingFunctionNone to suppress the labels:

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Put the labels above the points:

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Put them in a Tooltip:

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Label the points as ordered pairs:

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Label the points with their indices:

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LabelingSize  (3)

Textual labels are shown at their actual sizes:

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Specify a maximum size for textual labels:

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Image labels are automatically resized:

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Specify a maximum size for image labels:

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Show image labels at their natural sizes:

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MaxPlotPoints  (1)

Use MaxPlotPoints to limit the number of points used:

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Mesh  (6)

Mesh requires at least one dataset to be Joined:

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The initial and final sampling meshes are typically the same:

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Interpolated data may introduce points:

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Use 20 mesh levels evenly spaced in the direction:

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

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Use explicit styles at specific points:

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MeshFunctions  (3)

MeshFunctions requires at least one dataset to be Joined:

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

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

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MeshShading  (7)

MeshShading requires at least one dataset to be Joined:

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

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Use None to remove segments:

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MeshShading can be used with PlotStyle:

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MeshShading has higher priority than PlotStyle:

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Use PlotStyle for some segments by setting MeshShading to Automatic:

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MeshShading can be used with ColorFunction:

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PlotHighlighting  (7)

Plots have interactive coordinate callouts with the default setting PlotHighlightingAutomatic:

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Use PlotHighlightingNone to disable the highlighting for the entire plot:

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

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

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

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

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

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Specify the style for the points:

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

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Use Callout options to change the appearance of the label:

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Combine components to create a custom effect:

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PlotLabel  (1)

Add an overall label to the plot:

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PlotLabels  (5)

Specify text to label sets of points:

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Place the labels above the points:

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Use callouts to identify the points:

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Use the keys from an Association as labels:

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Use None to not add a label:

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PlotLegends  (6)

Generate a legend using labels:

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Generate a legend using placeholders:

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Legends use the same styles as the plot:

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Use Placed to specify the legend placement:

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Place the legend inside the plot:

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Use PlotLegends to change the appearance:

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PlotMarkers  (8)

ComplexListPlot normally uses distinct colors to distinguish different sets of data:

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Automatically use colors and shapes to distinguish sets of data:

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Use shapes only:

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Change the size of the default plot markers:

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Use arbitrary text for plot markers:

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Use explicit graphics for plot markers:

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Use the same symbol for all the sets of data:

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Explicitly use a symbol and size:

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PlotRange  (4)

PlotRange is automatically calculated:

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Show the whole dataset:

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Explicitly choose the x and y ranges:

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

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PlotStyle  (7)

Use different style directives:

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By default, different styles are chosen for multiple datasets:

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Explicitly specify the style for different datasets:

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PlotStyle applies to both curves and points:

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PlotStyle can be combined with ColorFunction:

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PlotStyle can be combined with MeshShading:

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MeshStyle by default uses the same style as PlotStyle:

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PlotTheme  (2)

Use a theme with simple ticks and grid lines in a bright color scheme:

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Change the color scheme:

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PolarAxes  (2)

Add polar axes and polar grid lines:

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Control the radial and polar axes independently:

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PolarAxesOrigin  (2)

Specify the angular axes and radial axes to intersect at :

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Place radial axes at the right of the graph:

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PolarGridLines  (2)

Use automatically chosen polar grid lines:

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Draw grid lines at the specified positions:

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PolarTicks  (4)

Place polar tick marks and labels automatically:

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Modify the angular ticks:

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Indicate angles with degrees:

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Place polar tick marks at the specified positions:

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ScalingFunctions  (3)

A single scaling function scales the data radially:

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

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None indicates no scaling in the specified direction:

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Ticks  (9)

Ticks are placed automatically for each axis:

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Use TicksNone to draw axes without any tick marks:

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

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Place tick marks at specific positions:

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Draw tick marks at the specified positions with specific labels:

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

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

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

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Specify a style for each tick:

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

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TicksStyle  (4)

By default, the ticks and tick labels use the same styles as the axis:

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Specify an overall ticks style, including the tick labels:

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Specify ticks style for each of the axes:

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

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

Plot roots of unity:

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Plot a discrete time signal and its spectrum:

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Graph zeros of the zeta function:

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Graph eigenvalues of a Cauchy matrix:

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Graphs solutions of :

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Show Gershgorin discs and eigenvalues for a matrix:

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

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Visualize iterations of Newton's method:

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

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Properties & Relations  (9)Properties of the function, and connections to other functions

Use ListPlot, ListLinePlot or ListPolarPlot for real data:

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ComplexListPlot is closely related to ListPlot:

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

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Use ComplexPlot3D to use the axis for the magnitude:

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Use ComplexArrayPlot for arrays of complex numbers:

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

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ComplexContourPlot plots curves over the complexes:

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ComplexRegionPlot plots regions over the complexes:

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ComplexStreamPlot and ComplexVectorPlot treat complex numbers as directions:

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Possible Issues  (2)Common pitfalls and unexpected behavior

Real-valued data is plotted along the axis.:

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

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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 20102011 regular season:

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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:

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

Graphically represent the integer as the point in the complex plane and connect the dots between the points representing and TemplateBox[{{m,  , x}, n}, Mod]:

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

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Use multiples of three and five instead:

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Out[5]=5
Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2023).
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Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2023).

Text

Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2023).

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Wolfram Research (2019), ComplexListPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/ComplexListPlot.html (updated 2023).

CMS

Wolfram Language. 2019. "ComplexListPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/ComplexListPlot.html.

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Wolfram Language. 2019. "ComplexListPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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

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Wolfram Language. (2019). ComplexListPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComplexListPlot.html

BibTeX

@misc{reference.wolfram_2024_complexlistplot, author="Wolfram Research", title="{ComplexListPlot}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexListPlot.html}", note=[Accessed: 08-January-2025 ]}

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@misc{reference.wolfram_2024_complexlistplot, author="Wolfram Research", title="{ComplexListPlot}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/ComplexListPlot.html}", note=[Accessed: 08-January-2025 ]}

BibLaTeX

@online{reference.wolfram_2024_complexlistplot, organization={Wolfram Research}, title={ComplexListPlot}, year={2023}, url={https://reference.wolfram.com/language/ref/ComplexListPlot.html}, note=[Accessed: 08-January-2025 ]}

Copy to clipboard.
@online{reference.wolfram_2024_complexlistplot, organization={Wolfram Research}, title={ComplexListPlot}, year={2023}, url={https://reference.wolfram.com/language/ref/ComplexListPlot.html}, note=[Accessed: 08-January-2025 ]}