Q. If $x + i y = \frac{a + ib}{a - ib}$ , then $x^{2} + y^{2} =$

1152 227 Complex Numbers and Quadratic Equations Report Error

A

$1$

50%

B

$2$

19%

C

$0$

22%

D

$4$

9%

Solution:

We have, $x + i y = \frac{a + ib}{a - ib}$
Taking modulus both sides, we get
$x^{2} + y^{2} = 1$
$\Rightarrow x^{2} + y^{2} = 1$