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2bornot2b
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How do we figure out what is going to be the domain of the log function for complex numbers? It is easy to figure out for inverse trigonometric functions, since we can draw the graph. But how to do the same for log function?
 2 years ago
 2 years ago
2bornot2b Group Title
How do we figure out what is going to be the domain of the log function for complex numbers? It is easy to figure out for inverse trigonometric functions, since we can draw the graph. But how to do the same for log function?
 2 years ago
 2 years ago

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2bornot2b Group TitleBest ResponseYou've already chosen the best response.0
@TuringTest can you help?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I am terrible at complex analysis... I also didn't get that @ you sent me; I better post that in feedback :S
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
looks like all numbers ... excluding zero.
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.0
Thanks for coming!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
very welcome! if only I could help ....
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.0
@experimentX The function is a multiple valued function, so there must be an interval. According to my book it says the interval is pi to +pi, my question was, how to find that range. I hope now I have clarified the thing.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
I was talking about log for complex values. Inverse Trigonometric functions have range pi to pi, because they are (they are periodic ... period of 2pi) < any value in terms of pi can be expressed in terms of pi and +pi dw:1335459261795:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
and of course it must be multivariable function (not a function)
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.0
Yes, that is exactly what I am searching for. For sin inverse, you can easily see from the picture what is going to be the range for principle value. And I have been taught to figure that out seeing the plot of sin inverse. But here in log z, how do I find the range for principle value. That is my question.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
in a same way we say sin(pi/2) = sin(2pi + pi/2) = sin(4pi + pi/2) = sin(6pi + pi/2) = 1 arcsin(1) = pi/2, 2pi+pi/2, 4pi + pi/2, ...
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
now let's check for log, the domain is going to be all comples plane except 0 ln(z) = ln(e^(lnz + iarg(z)) = lnz + i arg(z)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
as long as z != zero, i think we will have all values of complex plane as our domain.
 2 years ago
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