Complex Analysis: Theory and Applications · Problem 3.1.6

Analytic and Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · logarithmic-derivative

Problem

Let PP be a polynomial of degree 2, given by P(z)=(z−z1)(z−z2),P(z) = (z - z_1)(z - z_2), where z1≠z2z_1 \neq z_2. Show that P′(z)P(z)=1z−z1+1z−z2.\frac{P'(z)}{P(z)} = \frac{1}{z - z_1} + \frac{1}{z - z_2}. Note: The quotient P′(z)P(z)\dfrac{P'(z)}{P(z)} is known as the logarithmic derivative of PP.

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