Describing the Image of a Complex Function on the Unit Circle

[naggy]

How do I describe the image of a function like.
f(z) = (z-i)/(z+i) given that the length of z is equal to one. The domain is the unit circle.

Is the best way just let z=x+yi and then see what comes out? Or is there a simpler way of doing it.

 

[tiny-tim]

How do I describe the image of a function like.
f(z) = (z-i)/(z+i) given that the length of z is equal to one. The domain is the unit circle.

Is the best way just let z=x+yi and then see what comes out? Or is there a simpler way of doing it.

Hi naggy!

Hint: always get rid of the complex bit from the bottom if you can …

so multiply top and bottom by (z + i)bar