Question: complex number problem please help Let p(z), q(z) be analytic functions on the region |z z0| < R for some R > 0. In addition,

complex number problem

please help

Let p(z), q(z) be analytic functions on the region |z z0| < R for some R > 0. In addition, p(z0) not equal 0, and q(z) has a ZERO of order 2 at z0. (i) Prove that p(z)/q(z) has a pole of order 2 at z0. (ii) Compute Resz=z0 p(z)/q(z) in terms of p, q and their derivatives at z0.

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