Question

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

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

Answer 1

The correct option is C $1$

$z^4+z^3+z^2+z^2+z+1=0$
$\Rightarrow z^2(z^2+z+1)+1(z^2+z+1)=0$
$\Rightarrow (z^2+z+1)(z^2+1)=0$
$\therefore z=i,-i,w,w^2$. For each, $|z|=1$