- #1

Destroxia

- 204

- 7

## Homework Statement

Write the given numbers in the polar form ##re^{i\theta}##.

## \frac {2i} {(3e^{4+i})} ##

## Homework Equations

## z = re^(i\theta) ##

## \theta = Arg(z) ##

## r = |z| = \sqrt { x^2 + y^2 } ##

## The Attempt at a Solution

I'm not really sure how to go about the exponential on the bottom of form ## e^z ##. I've read through my book now about 10 times, and don't see any info on it in any of the chapters before the problem.

If you asked me I would say the bottom was already in polar form, but that doesn't seem correct due to the form being of ## e^{x+iy} ## instead of ## e^{i\theta} ##. I also know I can rewrite ## e^{x+iy} ## as ## e^x(cos(y)+isin(y)) ##, I believe. But I'm not sure that is going to help me.

The only thing I can really do at this point is find ## Arg(z) ## for ##2i## which ends up coming out to ## + \frac \pi 2 ##. I'm not sure how to algebraically manipulate these equations to combine them to the form of ## x + iy ## so I can convert find my ## Arg(z) ## for ## e^{4+i} ##, and then I can combine the Args through the property ## Arg(\frac {z_1} {z_2}) = Arg(z_1) - Arg(z_2) ##, as well as find the total ## |z| ##, and rewrite in polar form ##|z|e^{i\theta}##