- #1

rock.freak667

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## Homework Statement

Find an equation connecting x and y for which (z-1)/(z+1) has an argument [itex]\alpha[/itex]

## Homework Equations

z=x+iy

arg(z)=tan

^{-1}(y/x)

## The Attempt at a Solution

[tex]\frac{z-1}{z+1}[/tex]

Substituting z=x+iy

[tex]\Rightarrow \frac{z-1}{z+1}=\frac{(x-1)+iy}{(x+1)+iy}[/tex]

Realizing

[tex]\frac{(x+1)(x-1)+iy(x+1)-iy(x-1)-i^2y^2}{(x+1)^2+y^2}[/tex]

Re:i

^{2}=-1

[tex]= \frac{x^2+y^2-1}{(x+1)^2+y^2} +i \frac{2y}{(x+1)^2+y^2}[/tex]

Thus

[tex]tan\alpha = \frac{2y}{x^2+y^2-1}[/tex]

Is this correct? Or should I just put in the form of a circle?