I'm stuck on this question:

For the transformation:

w=(z+i)/(z-i)

show that as z moves along the real axis, w moves along a circle centre O and radius 1.

I know that since z only moves on the real axis, it has only an x component, so I can replace z with x, but I'm stuck after that. Do I rewrite w as u+iv? If so I get a very complicated equation which doesn't look like the equation of a circle. I'd be grateful of any help.