Complex Analysis

1. Let P(z) be a polynomial of degree 1. Let C(O; R) be the circle traversed in the counterclockwise direction with center 0 and radius R that encloses three points a, b and u. (a) Show that P(5) JC(0;R) (5 - a)(5-6)(5-2) d - 0 as R -+ co. (b) Deduce from (a) that P(u) P(a) P(b) (u - a)(u - b) - (a -b)(u- a) + (b - a)(u-b) '