## Loser66 one year ago Check my stuff, please. z = i w = -1 +i zw = -1-i

1. anonymous

Ill help Brb

2. Loser66

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

3. anonymous

Nevermind I cant help But I give Medal And Fan Sry

4. Loser66

@Empty

5. Empty

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

6. Loser66

what is log (zw) ?

7. Loser66

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 :(

8. Empty

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: $z=re^{i(\theta + 2 \pi n)}$ $\log(z) =\log (re^{i(\theta + 2 \pi n)}) = \log (r) + i(\theta + 2 \pi n)$

9. anonymous

your'e correct

10. Empty
11. Empty

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

12. Loser66

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

13. Loser66

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

14. Empty

$\frac{\pi}{2}=\frac{2 \pi}{4}$ $\frac{2 \pi}{4} + \frac{3 \pi}{4} = \frac{5 \pi}{4}$

15. Loser66

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

16. Loser66

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