Question

pls refer the picture for the question.​

Answer 1

${ \bold{ \underline{given} : - }} \\ \\ { \bold{x + iy = \frac{ {( {a}^{2} + 1) }^{2} }{2a - i}}} \\ \\ \\ \\ { \bold{ \underline{to \: \: find} : - }} \\ { \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + {y}^{2} }} \\ \\ \\ { \bold{ \huge{ \underline{solution} : - }}} \\ \\ { \bold{ \implies \: x + iy = \frac{ {( {a}^{2} + 1) }^{2} }{2a - i} }} \\ \\ { \bold{ \implies \: x - iy \: \: = \frac{ {( {a}^{2} + 1)}^{2} }{2a + i} }} \\ \\ \\ { \bold{ \: \: \: \: . \: \: now \: \: multiply \: \: these \: \: equation - }} \\ \\ { \bold{ \implies {x}^{2} - {(i)}^{2} {y}^{2} = \frac{ {( {a}^{2} + 1) }^{4} }{(2a + i)(2a - i)} }} \\ \\ { \bold{ \implies \: {x}^{2} + {y}^{2} = \frac{ { ({a}^{2} + 1) }^{4} }{ {4 {a}^{2} + 1} } }}$