Question

If `x + i y = \frac { a + i b } { a - i b }`, how do you prove that `x ^ { 2} + y ^ { 2} = 1`?

Answer 1

See below.

Explanation:

If `x + i y = \frac { a + i b } { a - i b }` then

`x-iy = (a-ib)/(a+ib)` its conjugate. So

`(x+iy)(x-iy)=x^2+y^2=1`