Question

If $a,b,c$ and $d\in R$ such that $a^2+b^2=4$ and $c^2+d^2=2$ and if $(a+ib{)}^2=(c+id{)}^2(x+iy)$, then $x^2+y^2$ is equal to

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (A)

Given, $(a+ib{)}^2=(c+id{)}^2(x+iy)$
$\Rightarrow |a+ib{|}^2=|c+id{|}^2|x+iy|$
$\Rightarrow a^2+b^2=\left(c^2+d^2\right)\left(\sqrt{x^2+y^2}\right)$
$\Rightarrow 4=2\left(\sqrt{x^2+y^2}\right)$
($\because a^2+b^2=4$ and $c^2+d^2=2$ given )
$\Rightarrow \sqrt{x^2+y^2}=2$
$\Rightarrow x^2+y^2=4$