Correct Answer - Option 1 :
\(\sqrt {\frac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}}\)
Calculation:
Given, \(x + iy = \sqrt {\frac{{a + ib}}{{c + id}}}\)
Taking modulus both sides:
\(\left| {x + ij} \right| = {\left| {\frac{{a + ib}}{{c + id}}} \right|^{\frac{1}{2}}}\)
\(\Rightarrow \sqrt {{x^2} + {y^2}} = {\left( {\frac{{\sqrt {{a^2} + {b^2}} }}{{\sqrt {{c^2} + {d^2}} }}} \right)^{\frac{1}{2}}}\)
\(\Rightarrow {x^2} + {y^2} = \frac{{\sqrt {{a^2} + {b^2}} }}{{\sqrt {{c^2} + {d^2}} }}\)