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[FP2] - Inequalities carried through Complex Transformations

The transformation T from the z-plane (x+iy) to the w-plane (u+iv) is given by:
T: w=16/z

The transformation maps the points of the circle |z-4|=4 in the z-plane, onto a line in the w-plane.

I've found that the line is u=2.

However, i now have the shade on an Argand Diagram the region for which: |z-4|< 4 when it is transformed under T.

How do i carry this inequality through the transformation?

Reply 1

Mark13

Original post by minnigayuen

You know that the interior of the circle is mapped to either the left or right side of the line u=2. See what happens to a point in the interior, like z=4 - this will tell you which side of the line the interior is mapped to.