Cauchy integral problem: can this answer be simplified further?

1. Nov 29, 2004

redshift

The question calls for using Cauchy's integral formula to compute the integral for Int.c z/[(z-1)(z-3i)] dz, assuming C is the loop |z-1|=3.
Taking z = 1 and f(z) = z/(z-3i), I came up with (2pi*i)/(1-3i), which seems like it could be simplified, but I'm not sure how.

2. Nov 29, 2004

xepma

Multiply the numerator and denominator with the complex conjugate of 1-3i = 1+3i. Than you will get rid of the 'i' in the denominator.