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

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