- #1
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Homework Statement
Given [tex]Z=\frac{z-2}{z}[/tex], if [tex]|z|=1[/tex] prove that the locus of Z is another circle whose centre and radius must be determined. Also describe the direction of Z as z describes the unit circle in an anticlockwise direction.
Homework Equations
[tex]z=x+iy[/tex]
The Attempt at a Solution
[tex]Z=\frac{x+iy-2}{x+iy}(\frac{x-iy}{x-iy})[/tex]
expanded and simplified: [tex]\frac{x^2-2x+y^2+i2y}{x^2+y^2}[/tex]
I think since [tex]|z|=1[/tex] then [tex]x^2+y^2=1[/tex]?
This leaves [tex]-2x+i2y[/tex] and I am completely lost at this point...