Question

If $z$ is a complex number satisfying $z^{2}+\frac{3}{z^{2}}=-4$ , then the sum of the absolute values of the imaginary parts of the roots of the equation is

• A. $0$
• B. $2\sqrt{3}$
• C. $2$
• D. $2\sqrt{3}+2$

Answer 1

Answer: (D)

$z^{4}+4z^{2}+3=0$
$\left(z^{2} + 1\right)\left(z^{2} + 3\right)=0$
$\Rightarrow z^{2}=-1$ or $-3$
$\Rightarrow z=\pm i,\pm\sqrt{3}i$
Hence, the required sum is $\left|1\right|+\left|- 1\right|+\left|\sqrt{3}\right|+\left|- \sqrt{3}\right|$