Complex Analysis: Theory and Applications · Problem 10.8.5

Applications of Harmonic Functions — Howell & Matthews

Mathematics — Complex Analysis · joukowski-ray-arc-mapping

Problem

Let R0R_0 be a ray through the origin inclined at an angle β0\beta_0. (a) Show that the image of the ray R0R_0 under w=2+2z1−zw = \dfrac{2+2z}{1-z} is an arc A0A_0 of a circle that passes through 22 and −2-2. (b) Show that the arc A0A_0 is inclined at the angle β0\beta_0.

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