Here we have two planes: z = x+ iy plane and w = u+ iv plane. First consider a branch cut for the term z = (w2 1)1/2 as it is a multivalued function. Now, consider the conformal map given by z = = f(w): f (w) = z = (w? 1)/2 + w To help solve this problem, consider w = g(z). From this, prove that z = diagram for both the z and w plane and show all working. Thus, f(w) transforms the u axis into part of the r axis for |2| > 1 plus the unit circle |2| = 1. Draw a diagram for both the z and w plane. f (w) transforms the u axis into the part of the r axis for |2| >1 plus the unit circle |z| = 1. Draw a