# Complex Numbers

by conorordan
Tags: complex, numbers
 P: 13 1. The problem statement, all variables and given/known data "The transformation T from the z-plane to the w-plane is given by $w=\frac{1}{Z-2}$ where $Z=x+iy$ and $w=u+iv$ Show that under T the straight line with equation $2x+y=5$ is transformed to a circle in the w-plane with centre $\left ( 1,-\frac{1}{2} \right )$ and radius $\frac{\sqrt{5}}{2}$ 3. The attempt at a solution I've worked out that the line $2x+y=5$ can be written in locus form as $\left|Z-10\right|=\left|Z+10-10i\right|$