Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 ComplexToPolar

Source Notebook

Get a complex number in polar form or polar exponential form

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["ComplexToPolar"][z]

returns the complex number z in polar exponential form.

ResourceFunction["ComplexToPolar"][z,type]

returns the complex number z with the form type.

Details and Options

For numeric input, ResourceFunction["ComplexToPolar"] returns a complex number in an Inactive form. For symbolic input, ResourceFunction["ComplexToPolar"] returns unevaluated.
Possible types include All, "Polar" and "Exponential".
The polar form of a complex number is z=r(cos θ+i sin θ) where r and θ are real.
The exponential form of a complex number is z=reiθ where r and θ are real.

Examples

Basic Examples (4) 

Return a polar exponential form for a numeric quantity:

In[1]:=
ResourceFunction["ComplexToPolar"][1 - 2 I]
Out[1]=

Specify that you want the number in polar form:

In[2]:=
ResourceFunction["ComplexToPolar"][1 + I, "Polar"]
Out[2]=

Specify that you want the number in polar exponential form:

In[3]:=
ResourceFunction["ComplexToPolar"][1 - I, "Exponential"]
Out[3]=

Return all forms as an Association:

In[4]:=
ResourceFunction["ComplexToPolar"][-Sqrt[2], All]
Out[4]=

Scope (1) 

For symbolic input, ComplexToPolar returns unevaluated:

In[5]:=
ResourceFunction["ComplexToPolar"][a + b I]
Out[5]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.0.0 – 11 May 2020

Author Notes

To view underlying source code, evaluate the following:

In[1]:=
SystemOpen[ FileNameJoin[ ReplacePart[ FileNameSplit[FindFile["ResourceFunctionHelpers`"]], -1 -> "ComplexToPolar.wl"]]]

License Information