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@TuringTest can you help?
I am terrible at complex analysis... I also didn't get that @ you sent me; I better post that in feedback :S
looks like all numbers ... excluding zero.
Thanks for coming!
very welcome! if only I could help ....
@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.
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|
and of course it must be multivariable function (not a function)
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.
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, ...
now let's check for log, the domain is going to be all comples plane except 0 ln(z) = ln(e^(ln|z| + iarg(z)) = ln|z| + i arg(z)
as long as |z| != zero, i think we will have all values of complex plane as our domain.