How to Write e^e^i on the Form a + bi: Using Log and Other Methods for Homework

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Homework Statement



I want to write e^e^i on the form a + bi

Homework Equations



I think I have to use log

The Attempt at a Solution



Well I've tried to use log, but there's probably an easy way, but I just can't figure it out.



btw does someone know whether you can use latex or some other graphic language because its pretty hard to express yourself math wise
 
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e^{i\theta} = Cos\theta + iSin\theta

That should help signifigantly.and about the Latex thing, click the "go advanced" tab when you reply to a message, of start a new thread or topic / whatever, and click the button that has a Sigma on it. it should be the last one on the bottom row on the right.
 
ty!...
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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