How can i solve , where is any complex number?

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- Nov 27th 2012, 02:48 PMtenderlinecomplex equation with exponential
How can i solve , where is any complex number?

- Nov 27th 2012, 06:54 PMhollywoodRe: complex equation with exponential
.

The log is the complex log, which is multiple-valued: , where n is any integer.

And .

Is that what you were asking?

- Hollywood - Nov 28th 2012, 12:11 AMtenderlineRe: complex equation with exponential
my problem, in its completeness, is the following: i'm looking for singularities of a function whose denominator is . So i look for solutions of . I put where is the principal branch of complex logarithm and by periodicity of complex exp i get , where log in RHS is the real log. So and i was looking for an easy way to write the RHS in order to compute residues at those points

- Nov 28th 2012, 07:48 AMhollywoodRe: complex equation with exponential
Since and are both real, you can do what I suggested in my previous post:

Other than that, I don't really see how to simplify it.

- Hollywood