you will Start with z=cos(x)+isin(x)......(1) , = iz
so dz/z=idx , in (z) = ix+c from (1); when x=0 | z=1 so c=0
in (z) = ix
z=e^(ix) but z= cos (x)+isin
so cos (x)+isin (x) = e^ (ix) (x) , Put x=pi in (z) & we get
ANSWER = -1+0=e^(ip) , so it is = e^(ipi)+1=0
Dose this help you in any way?