To calculate the inverse value (1/z) we multiply the top and bottom by the conjugate which makes the denominator a real number.
| z plane | w plane | |
|---|---|---|
 |
--> w=1/z |
|
Let the components of the input and output planes be:
z = x + D y and w = u + D v
In this case w = 1/z
so:
w = 1/(x + D y)
As usual, we evaluate the inverse by multiplying top and bottom by the conjugate:
w = (x - D y)/(x + D y)(x - D y)
w = (x - D y)/(x² - y²)
so the u and v components are:
u = x /(x²-y²)
v = -y /(x²-y²)
