Question

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

• A. $|\omega |$
• B. $\frac{3}{4}$
• C. $|\pm i|$
• D. None of these

Answer 1

Answer: (A), (C)

Given $z^4+z^3+2z^2+z+1=0$
$\Rightarrow (z^2+z+1)(z^2+1)=0$
$\Rightarrow z=\omega ,{\omega }^2,i,-i$
for each value of $z,|z|=1$