# Complex numbers

posted by
**Jake** on
.

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 do not know where to start

changing it to polar form will help

w=magnitude @ (arctan 1/z - arctan -1/z)

where magnitude is sqrt (z^2+1)/(z^2+1)

or

w= 1 @ (2 arctan 1/z)

Is that a circle?

check my thinking.

I am really sorry but I do not understand your notation

please I need further help