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 2 years 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?
 2 years 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?

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

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

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

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

2bornot2b
 2 years ago
Best 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.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1I 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

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

2bornot2b
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, 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.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1in 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, ...

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1now 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)

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