What Are the Solutions for e^z in Complex Numbers?

[stihl29]

Homework Statement

e^z = e
e^z = e^-z

Homework Equations

they are the first 2 questions on my homework and my book is so bad i don't even know how to get the right answers, I've been online for over an hour I'm i'm sure they are easy.

The Attempt at a Solution

ffirst one just guessing ?
z = 1 ?
second in the back of the book says z = i*k*pi k = 1, 2, 3..

 

[Office_Shredder]

What can you say about e^x+iy for x and y real numbers?

 

[stihl29]

e^x(cos(y) + isin(y)) = e??
i got that ones, i feel like I'm being really dumb and just not seeing something really simple

 

[Office_Shredder]

What? That doesn't make any sense. You should review how to calculate e^x+iy by splitting it up into e^xe^iy and calculating e^iy