having trouble with a complex numbers problem

Question

I'm pretty good at this stuff, but sometimes I come across questions like this:

$$e^z = e^w, \quad z, w \in \mathbb{C}.$$

choose the correct answers:

A: $z=w$

B: $|z| = |w|$

C: $e^{iz} = e^{iw}$

D: $e^{2z} = e^{2w}$

can anyone explain what are the correct answers and why?

thanks!

score 5 · Answer 1 · answered Dec 07 '13 at 18:19

5

Hint: Consider the complex numbers $z=0$ and $w=i 2 \pi$ and check every option. What do you find?

answered Dec 07 '13 at 18:19

Mark Fantini

score 2 · Answer 2 · answered Dec 07 '13 at 18:19

2

Hint for all:

$$z=0\,,\;\,w=2\pi i$$

answered Dec 07 '13 at 18:19

DonAntonio

so D is correct only? – user2970357 Dec 07 '13 at 18:32
ah ok i got it... thanks don and fantini for the hint! – user2970357 Dec 07 '13 at 18:35

2 Answers2