0
$\begingroup$

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?

  • 1
    If you cannot apply the theorem, this does not mean that the zero cannot arise as a result. Simply you cannot predict the result.2012-09-15
  • 0
    In fact, the standard parameterization of the circle gives integral 0. But parameterizing each side of the square by _x_ or _y_, as appropriate, gives sum of integrals on the sides to be 4 _i_.2012-09-15

1 Answers 1