BUILT-IN MATHEMATICA SYMBOL

Arg

Arg[z]
gives the argument of the complex number z.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

Arg[z] is left unevaluated if z is not a numeric quantity.

Arg[z] gives the phase angle of z in radians.

The result from Arg[z] is always between and .

Arg[z] has a branch cut discontinuity in the complex z plane running from to 0.

Arg gives 0.

Arg automatically threads over lists.

EXAMPLES

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Basic Examples (2)

The result is given in radians:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

In[1]:=

Out[1]=

Scope (4)

For purely real or imaginary arguments, exact results are returned:

For generic approximate complex arguments, approximate results are returned:

The precision of the output tracks the precision of the input:

Arg threads element-wise over lists and matrices:

Generalizations & Extensions (3)

Arg returns exact answers for exact numerical arguments:

Infinite arguments give symbolic results:

Arg threads element-wise over sparse arrays:

Applications (3)

Polar decomposition of a complex number:

Color a plot according to value of Arg:

Expand multivalued functions without making assumptions about variables:

Properties & Relations (6)

Simplify expressions containing Arg:

Generate Arg from FullSimplify:

Use Arg as a target function in ComplexExpand:

Rescale Arg to run from 0 to 1:

Find the domain of positivity for a linear function:

Use Arg to specify assumptions about complex variables:

Possible Issues (3)

Degenerate cases give intervals as results :

Numerical decision procedures with default settings cannot simplify this expression:

The machine-precision result is incorrect:

The arbitrary-precision result indicates that the result may be incorrect:

Using a larger setting for $MaxExtraPrecision gives the correct result:

The input contains a hidden zero, and simplifying the argument gets the correct answer:

The argument principle of complex analysis cannot be used because Arg has range

:

Neat Examples (1)