I'm posting with my phone so I cannot using latex. I will be thankful if somebody correct my post.
I want to integrate $x^2-iy^2$ on the complex plane with
(a) closed unit circle
(b) closed unit square $(+1+i, 1-i, -1+i, -1-i)$
By my calculation, the answers are same; zero. But the integrand is not analytic so I cannot use Cauchy integral theorem. Then how can I explain this situation?