hey all, i got this problem

find all the solutions z^(i)=1

so i wrote it out as e^(i(ln(1)+i@)= 1

@= theta

and i end up getting e^(-@)=1

is that right?

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- Feb 28th 2010, 08:09 PM #1

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- Mar 1st 2010, 04:35 AM #2

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- Mar 1st 2010, 05:53 AM #3

- Mar 1st 2010, 06:02 AM #4

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This question also appeared in this thread.

To complete the answer I gave there (since Tonio's answer is incorrect): is equivalent to (up to this point, the values of the left-hand sides depend on the determination of the logarithm), which is equivalent to for some , and thus to , . Hence the solutions are the real numbers for every ; it is worth noting that since the answer is real, the choice of the determination of the logarithm is irrelevant (and you can forget about it if you don't know what I mean).

Edit: drumist was quicker than me, but I leave my post because of the remark on the definition of logarithm

- Mar 1st 2010, 12:57 PM #5

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