- #1
genjix
- 3
- 0
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}.
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.
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.