Question

If $x+iy=\sqrt{\frac{a+ib}{c+id}},$ then $(x^2+y^2{)}^2$ equals

• A. $\frac{a^2-b^2}{c^2+d^2}$
• B. $\frac{a^2+b^2}{c^2+d^2}$
• C. $\frac{(a-b)(c-d)}{(a+b)(c+d)}$
• D. None of these

Answer 1

The correct option is B $\frac{a^2+b^2}{c^2+d^2}$

Given $x+iy=\sqrt{\frac{a+ib}{c+id}}...\left(i\right)$
$\therefore x-iy=\sqrt{\frac{a-ib}{c-id}}...\left(ii\right)$
$\therefore$ Multiplying (i) and(ii) we get $x^2+y^2=\sqrt{\frac{a^2+b^2}{c^2+d^2}}$
$\Rightarrow (x^2+y^2{)}^2=\frac{a^2+b^2}{c^2+d^2}$