I am trying to calculate the contour integral of the complex conjugate of z around a square with sides of length 2 centred on the origin in the complex plane
∫ f(z) dz = ∫ f(t) (dz/dt) dt . It looks like the integral signs won't appear here but they should be at the front of each side of the equation
The Attempt at a Solution
I already know the answer is 2π I and calculate this answer using polar form but when I calculate it around the square I get the answer to be 4 x 2i. Each of the sides contributes 2i. I can't get π to appear anywhere in my answer.
If I take the right hand vertical side , I parametrise it as z = 1 + i(t-1) so dz/dt = i and the complex conjugate of z is 1-i(t-1) so I get the integral with limits 2 and 0 of i+1-t which gives 2i.
What am I doing wrong and how do I get π to appear ?