Complex Analysis: Theory and Applications · Problem 6.2.8

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · contour-integrals-circles

Problem

Let

f

be a continuous function on the circle

\{z : |z - z_0| = R\}

. Show that

\int_{C_R^+(z_0)} f(z)\,dz = iR\int_0^{2\pi} f(z_0 + Re^{i\theta})e^{i\theta}\,d\theta.