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

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.2arg z = pi/2 arg w = 3pi/4 arg (zw) = 5pi/4, what is wrong with them?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nevermind I cant help But I give Medal And Fan Sry

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Nothing is wrong with them, arg(z)+arg(w)=arg(zw) in general.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2I 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 :(

Empty
 one year ago
Best ResponseYou've already chosen the best response.1Depends, 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: \[z=re^{i(\theta + 2 \pi n)}\] \[\log(z) =\log (re^{i(\theta + 2 \pi n)}) = \log (r) + i(\theta + 2 \pi n)\]

Empty
 one year ago
Best ResponseYou've already chosen the best response.1You're trying to prove a false statement as far as I can tell.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2(zw) = 1i, hence its argument is 5pi/4

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2and this argument is = arg z + arg w, right?

Empty
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\pi}{2}=\frac{2 \pi}{4}\] \[\frac{2 \pi}{4} + \frac{3 \pi}{4} = \frac{5 \pi}{4} \]

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2So, for those numbers, z and w. The statement is true. right? log (zw) = log z + log w

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Hence, to prove the statement is wrong, I have to pick other z, w, right?
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