# Find values of z

1. Feb 19, 2014

### alexcc17

1. The problem statement, all variables and given/known data
Find all values of z such that ez=1+i√3

2. Relevant equations

3. The attempt at a solution
I have no idea how to do this. I was going to start with ez=exeiy and try to figure something out from that, but I'm not seeing anything. I checked the solution shown below, but I'm really confused as to how they went from the equation given to the first step. An explanation would be really helpful.

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2. Feb 19, 2014

### Ray Vickson

If you write $1 + i \sqrt{3} = r e^{i \theta}$ (where you can easily figure out $r$ and $\theta$) then the equation is $e^{z} \equiv e^x e^{iy} = r e^{i \theta}$.