Mathematical Methods in the Physical Sciences · Problem 9.6

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · conformal-mapping-square-root

Problem

w = \sqrt{z}

. Hint: This is equivalent to

w^2 = z

; find

x

and

y

in terms of

u

and

v

and then solve the pair of equations for

u

and

v

in terms of

x

and

y

. Note that this is really the same problem as Problem 1 with the

z

and

w

planes interchanged.