If for all points in the complex plane then by Liouville's theorem the function is constant and so completing the proof.
The question goes this way:
(Q) The complex variable function f(z) is analytic in the complex plane, and |f(z)| < M, where M is a constant.
Prove that
I = ∫C f(z) / [(z-a)(z-b)] dz = 0,
where a, b are two different complex number, and C is the circle |z| = R, (R > |a|, R> |b|).
Let R→∞
Using residual theorem, I have only managed to reach this far:
I = 2πi {[f(a)-f(b)]/(a-b)}
Now, how do I prove that f(a)=f(b)?
Thanks.
If for all points in the complex plane then by Liouville's theorem the function is constant and so completing the proof.