Example 2.10. Show that the image of the open disk |z + 1+ i| < 1

under the transformation w = (3-4i)z + 6+2i is the open disk |w + 1-3i| < 5.

Solve for z in terms of w.

Solve for |z + 1+ i| < 1.

Which is the disk |w + 1-3i| < 5 in the w-plane.

Return to the Complex Analysis Project

 (c) John Mathews, 1998, 2006