Question

If x-iy=√a-ib/c-id prove that x^2+y^2=a^2+b^2/c^2+d^2

Answer 1

Answer:

$x - iy = \sqrt{ \frac{a - ib}{c - id} } \: \: \: \: \: \: ..............(1)\\ \\ x + iy = \sqrt{ \frac{a + ib}{c + id} } \: \: \: \: \: \: ..............(2) \\ \\ (1) \times (2) = > \\ \\ {x}^{2} - {i}^{2} {y}^{2} = \sqrt{ \frac{ {a}^{2} - {i}^{2} {b}^{2} }{ {c}^{2} - {i}^{2} {d}^{2} } } \\ \\ {x}^{2} + {y}^{2} = \sqrt{ \frac{ {a}^{2} + {b}^{2} }{ {c}^{2} + {d}^{2} } }$