Question

A circle in the z-plane has its center at z=3 and a radius of a radius of 2 units. Determine its image in w-plane when transformed by w=1/2.

Answer 1

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Answer on Question #55652 – Math – Complex Analysis

A circle in the z-plane has its center at $z=3$ and a radius of 2 units. Determine its image in w-plane when transformed by $w=1/2$.

Solution

Image in w-plane is $1/2$ when transformed by $w=1/2$.

Image in w-plane is a circle centered at $z=1.5$ and a radius of 1 when transformed by $w = \frac{1}{2} z$.