# complex rectangular to polar

I'm new to Sage. How do I convert a complex number like 2+3i into its polar form symbolically to get it in the form r.e^i.theta?

complex rectangular to polar

asked **
2013-10-26 00:25:45 -0500
**

Anonymous

I'm new to Sage. How do I convert a complex number like 2+3i into its polar form symbolically to get it in the form r.e^i.theta?

add a comment

1

You can use `abs()`

and `arg()`

functions to compute modulus and argument of a symbolic complex number as follows:

```
sage: a = 2 + 3*I
sage: b = abs(a)*e^(I*(arg(a))) ; b
sqrt(13)*e^(I*arctan(3/2))
sage: bool(a == b)
True
```

In the other direction, you can use `real_part()`

and `imag_part()`

```
sage: c = real_part(b) + I*imag_part(b) ; c
sqrt(13)*cos(real_part(arctan(3/2)))*e^(-imag_part(arctan(3/2))) + I*sqrt(13)*e^(-imag_part(arctan(3/2)))*sin(real_part(arctan(3/2)))
sage: c.simplify()
3*I + 2
```

Asked: **
2013-10-26 00:25:45 -0500
**

Seen: **874 times**

Last updated: **Oct 26 '13**

how to obtain the real part of a complex function

How does sage deal with choosing branches? Examples?

Weird output for differential of a non-analytic complex function.

Why is diff(conjugate(x),x) unevaluated?

Complex forms and differentials

Finding Re() and Im() for complex numbers

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.