## MIT 1803 lecture 6

This lecture introduced complex numbers – most of which I knew.  But useful to me was the reminder that, when presented with an integral like $\int e^{-x} \cos x dx$ one can solve it by passing to the complex domain, or complexifying the integral, that is, noting that the integrand is the Re part of a complex expression, solving the integral and pulling off the Re part of the answer.

$\int e^{-x} \cos x dx = Re [ \int e^{-x} { e^{ix} + e^{-ix} \over 2} dx ] = {1 \over -2e} ( \cos x - \sin x)$