Question

if
$x + yi = \sqrt{ \frac{a + ib}{c + id} }$
then proove that
$( {x}^{2} + {y}^{2} ) {}^{2} = \sqrt{ \frac{ {a}^{2} + {b}^{2} }{ {c}^{2} + {d}^{2} } }$
​

Answer 1

Step-by-step explanation:

$x + yi = \sqrt{ \frac{a + ib}{c + id} }$

...........(1)

therefore

$x - yi = \sqrt{ \frac{a - ib}{c - id} }$

.......(2)

multiplying (1) and (2)

we get,

${x}^{2} + {y}^{2} = \sqrt{ \frac{(a + ib)(a - ib)}{(c + id)(c - id)} }$

${x}^{2} + {y}^{2} = \sqrt{ \frac{ {a}^{2} + {b}^{2} }{ {c}^{2} + {d}^{2} } }$