Question

If z be a complex number satisfying$z^4+z^3+2z^2+z+1=0$ then $|z|$ is

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $1$
• D. None of these

Answer 1

The correct option is C $1$

$z^4+z^3+2z^2+z+1=0$
$[z^4+2z^2+1]+[z^3+z]=0$
$[z^2+1][z^2+1+z]=0$
$z^2+1=0⟹z=\pm i$
$\left|z\right|=1$
or
$z^2+z+1=0$
$z=\frac{-1\pm \sqrt{1-4}}{2}=\frac{-1\pm \sqrt{3i}}{2}$
$\left|z\right|=\sqrt{\frac{1}{4}+\frac{3}{4}}=1$
$\therefore \left|z\right|=1$