Question

Can someone help me integrate with an imaginary root in the function?

Answer 1

\[\int\limits_{0}^{\infty} e^{-5t-i2 \pi t} dt\] where i is imaginary. What do I do with the i?

Answer 2

\[\int\limits_{0}^{\infty} e^{-5t-i2 \pi f t} dt\]

Answer 3

sorry for the f in the equation which is just a constant

Answer 4

You treat it like a constant

Answer 5

oh okay do you know how I could integrate this though?

Answer 6

\[\int\limits_0^\infty e^{-5t-i 2\pi f t}dt=\int\limits^\infty_0 e^{-t(5+i2\pi f)}dt=\frac{1}{-5-i2\pi f}\int\limits_0^\infty e^{-t(5+i2\pi f)}d(-t(5+i2\pi f))\\=\frac{e^{-t(5+i2\pi f)}}{-5-i2\pi f}\]

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