Question: Show that the function where z = x + jy and w = u + jv, maps the circle |z| = 3 on the z

Show that the function

W w= z-1 z +1

where z = x + jy and w = u + jv, maps the circle |z| = 3 on the z plane onto a circle in the w plane. Find the centre and radius of this circle in the w plane and indicate, by means of shading on a sketch, the region in the w plane that corresponds to the interior of the circle |z|= 3 in the z plane.

W w= z-1 z +1

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