Find z for ez=1+i√3: Solution Explained

[alexcc17]

Homework Statement

Find all values of z such that e^z=1+i√3

Homework Equations

The Attempt at a Solution

I have no idea how to do this. I was going to start with e^z=e^xe^iy 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.

 

[Ray Vickson]

Homework Statement

Find all values of z such that e^z=1+i√3

Homework Equations

The Attempt at a Solution

I have no idea how to do this. I was going to start with e^z=e^xe^iy 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.

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