Hi, I just had my exam on complex analysis and would just like to know if I did this question correctly.(adsbygoogle = window.adsbygoogle || []).push({});

It said that the function [itex]f(z)[/itex] was analytic and to show that the integral of [itex]f(z)-\frac{c}{z}[/itex] existed for some constant c, then to find a formula for c in term of an integral of f(z).

I said consider the function [itex]w(z)=zf(z)-c[/itex], which is clearly analytic, then:

[itex]w(0)=\frac{1}{2\pi i }\oint \frac{zf(z)-c}{z}dz[/itex] by cauchys integral theorem

so the integral of the given function is simply equal to the function i defined by w evaluated at z=0

then from there I just split the integral into 2 integrals, one in terms of f(z) and the other in terms of c/z in which the constant can come out, and then the integrand would be equal to 2pik with k= winding number, given the contour didnt cross the origin and rearranged for c.

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# Complex analysis- show that the integral of this function exists

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