Help on simple Differential Calculus involving complex exponents

[Sleighty]

HI guys, I just started university and I have no idea what is going on in my lectures. My lecturer doesn't explain anything well and he is also the bloke who takes my tutorials. Lose - lose situation! Anyways I am trying to learn this myself, but I am stumped on this question:

Homework Statement

Find all solutions to the following equations:

i.) e^z = i
ii.)e^z = -10



A detailed solution would be helpful :) Also if you guys have any resources from which i can learn this, I would be greatful :)


-ash

 

[lanedance]

hey sleighty, welcome to PF, generally you need to have a go first & people will help you through it, but i'll help you get started...

first you can write z = x+iy, then
$$e^z = e^{x+iy} = e^x e^{iy}$$