Finding the Locus of z for R: A Real Number

[Mentallic]

Homework Statement

If R is a real number, find the locus of z defined by:

z=\frac{1+iR}{1-iR}

Homework Equations

z=x+iy

The Attempt at a Solution

z=(\frac{1+iR}{1-iR})(\frac{1+iR}{1+iR})

=\frac{1-R^2+i2R}{1+R^2}

Therefore, x=\frac{1-R^2}{1+R^2}

and y=\frac{2R}{1+R^2}

I'm unsure what to do now though...

 

[gabbagabbahey]

Hmmm... why not compute |z| and see if that gives you anything useful

 

[Mentallic]

Everything just fell into place and |z|=1. How did you know that would happen? lol