I'm doing a question where i have to calculate a the line integral; ∮z .dz over a simple closed contour, which as expected ( By Cauchy) came out as 0.

It's the supplementary questions that are confusing, i'm asked to calculate the integral with z replaced with the conjugate of z, and then to explain the relationship between these two integrals and the integrals over the same contour of just the real(z) and imaginary(z).

can someone shed some light on how they relate.

cheers