Given:
⇒ x + iy = \(\frac{a+ib}{a-ib}\)
We know that for a complex number Z=a+ib it’s magnitude is given by |Z| = \(\sqrt{a^2+b^2}\)
We know that \(|\frac{a}{b}|\) is \(|\frac{a}{b}|\)
Applying Modulus on both sides we get,
Squaring on both sides
⇒ \((\sqrt{x^2+y^2)^2}\) = 12
⇒ x2 + y2 = 1
∴ Thus Proved.