How can I use complex numbers to evaluate an integral? For instance I'm reading a book on complex numbers and it says that to evaluate the integral from 0 to pi { e^2x cos 4x dx }, I must take the real part of the integral from 0 to pi { e^((2 + 4i)x) dx}.(adsbygoogle = window.adsbygoogle || []).push({});

It totally skips how you do that. I don't see how taking the real part of the second integral relates to the first one. If I try to integrate e^((2 + 4i)x) and then take the real part, I eventually get:

Re(z) = 1/5 e^2x (1/2 cos 4x + sin 4x)

But I don't see any relation whatsoever, or how they did this.

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# Using complex numbers for evaluating integrals

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