Question

Check my stuff, please.
z = i
w = -1 +i
zw = -1-i

Answer 1

Ill help Brb

Answer 2

arg z = pi/2
arg w = 3pi/4
arg (zw) = 5pi/4,
what is wrong with them?

Answer 3

Nevermind I cant help But I give Medal And Fan Sry

Answer 4

@Empty

Answer 5

Nothing is wrong with them, arg(z)+arg(w)=arg(zw) in general.

Answer 6

what is log (zw) ?

Answer 7

I have to prove log (zw) \(\neq \) log z + log w because of their argument from both sides are not the same. But I don't see it :(

Answer 8

Depends, it's multivalued since \[e^{i \theta} = e^{i(\theta + 2 \pi)}\] we can do this an integer amount of times + or - so we have:
Every complex number has a polar form:
\[z=re^{i(\theta + 2 \pi n)}\]
\[\log(z) =\log (re^{i(\theta + 2 \pi n)}) = \log (r) + i(\theta + 2 \pi n)\]

Answer 9

your'e correct

Answer 10

http://math.stackexchange.com/a/927129/207119

Answer 11

You're trying to prove a false statement as far as I can tell.

Answer 12

(zw) = -1-i, hence its argument is 5pi/4

Answer 13

and this argument is = arg z + arg w, right?

Answer 14

\[\frac{\pi}{2}=\frac{2 \pi}{4}\]

\[\frac{2 \pi}{4} + \frac{3 \pi}{4} = \frac{5 \pi}{4} \]

Answer 15

So, for those numbers, z and w. The statement is true. right? log (zw) = log z + log w

Answer 16

Hence, to prove the statement is wrong, I have to pick other z, w, right?