यदि (if)` x+ iy =sqrt( ( a+ ib ) /( c+id) ` तो साबित कीजिए की (then prove that)
` (x^(2) +y^(2))^(2) =(a^(2)+ b^(2))/( c^(2) +d^(2))`

Explanation

प्रश्न से ,`x+ iy =sqrt(( a+ib)/(c+id) ) rArr (x+ iy)^(2) =(a+ ib)/( c+id) `
दोनों तरफ मापांक लेने पर ,`|( x+iy) ^ 2 | = | ( a + ib ) / ( c + id ) | `
`rArr | x + i y | ^ 2 = ( | a + ib| ) /(| c + id | ) [ because |z ^ n | = | z |^n ` तथा ` | ( z _ 1 ) /( z _ 2 ) | = ( | z _ 1| ) /( | z _ 2 | )] `
` rArr ( sqrt ( x ^ 2 + y ^ 2 ) ) ^ 2 = (sqrt ( a ^ 2 + b ^ 2 )) /( sqrt ( c ^ 2 + d ^ 2 )) rArr x ^ 2 + y ^ 2 = ( sqrt ( a ^ 2 + b ^ 2 ) ) /( sqrt ( c ^ 2 + d ^ 2 )) `
` rArr ( x ^ 2 + y^ 2 )^ 2 = ( a ^ 2 + b ^ 2 ) /( c ^ 2 + d ^ 2 ) `