Question

The values of $x$ and $y$ for which the numbers $3+i{x}^{2}y$ and $x^2+y+4i$ are conjugate complex, can be

• A. $(-2,-1)$ or $(2,-1)$
• B. $(-1,2)$ or $(-2,1)$
• C. $(1,2)$ or $(-1,-2)$
• D. None of these

Answer 1

Answer: (A)

$(-2,-1)$ or $(2,-1)$

Given, $3+i{x}^{2}y$ and $x^2+y+4i$ are conjugate.
$\therefore 3-i{x}^{2}y=x^2+y+4i$
$\Rightarrow x^2+y=3$ and $x^{2}y=-4$
$\Rightarrow x=\pm 2,y=-1$
$\therefore (x,y)=(2,-1)$ or $(-2,-1)$