Mathematical Methods in the Physical Sciences · Problem 10.11

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · orthogonal-circles-mapping

Problem

For

w = \ln\left[\dfrac{z+1}{z-1}\right]

, show that the images of

u = \text{const.}

and

v = \text{const.}

are two orthogonal sets of circles. Find centers and radii of five or six circles of each set and sketch them. Include the circle with center at the origin.

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