Consider the polynomials p(z), q(z) in the complex variable z and let
\(\rm I_{p, q}=\oint_\gamma p(z) \overline{q(z)} d z\)
where γ denotes the closed contour
γ(t) = eit, 0 ≤ t ≤ 2π. Then
1
\(\rm I_{z^m, z^n} = 0 \) for all positive integers m, n with m ≠ n
2
\(\rm I_{z^m, z^n} = 2\pi i\) for all positive integers n
3
Ip, 1 = 0 for all polynomials
4
\(\rm I_{p, q}=p(0) \overline{q(0)} \) for all polynomials p, q
5
Question Not Attempted