(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

z=x+iy

arg(z)=tan^{-1}(y/x)

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Checking the answer to complex number question

**Physics Forums | Science Articles, Homework Help, Discussion**