Question

If $z$ is a complex number satisfying $z^4+z^3+2z^2+z+1=0$, then the set of possible values of $|z|$ is

• A. $\{1,2\}$
• B. $\{1\}$
• C. $\{1,2,3\}$
• D. $\{1,2,3,4\}$

Answer 1

Answer: (B)

The given equation is $\left(z^2+z+1\right)\left(z^2+1\right)=0$
$\Rightarrow z=\pm i,\omega ,{\omega }^2$;
where $\omega$ being an imaginary cube root of unity.
Thus $|z|=1$.