Mathematical Methods in the Physical Sciences · Problem 9.5

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · conformal-mapping-sketching

Problem

For the function

w = f(z) = u + iv

, find

u

and

v

as functions of

x

and

y

. Sketch the graphs in the

(x, y)

plane of the images of

u = \text{const.}

and

v = \text{const.}

for several values of

u

and several values of

v

. The curves

u = \text{const.}

should be orthogonal to the curves

v = \text{const.}

w = \frac{z-i}{z+i}