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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?
 one year ago
 one year ago
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?
 one year ago
 one year ago

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2bornot2bBest ResponseYou've already chosen the best response.0
@TuringTest can you help?
 one year ago

TuringTestBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like all numbers ... excluding zero.
 one year ago

TuringTestBest ResponseYou've already chosen the best response.0
very welcome! if only I could help ....
 one year ago

2bornot2bBest 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.
 one year ago

experimentXBest 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
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
and of course it must be multivariable function (not a function)
 one year ago

2bornot2bBest 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.
 one year ago

experimentXBest 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, ...
 one year ago

experimentXBest 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)
 one year ago

experimentXBest 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.
 one year ago
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