Question

lf $z^4+z^3+2z^2+z+1=0$ then $|z|=$

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

Answer 1

The correct option is C $1$

$z^4+z^3+2z^2+z+1+0$

$\Rightarrow z^4+z^3+z^2+z^2+z+1=0$

$\Rightarrow z^2(z^2+z+1)+(z^2+z+1)=0$

$\Rightarrow z^2+z+1=0$ or $(z^2+1)=0$

$\Rightarrow (z-w)(z-w^2)=0$ or $\Rightarrow z=\pm i$

$\Rightarrow z=w,w^2$

So, $z=w,w^2,i,-i$

$\left|z\right|=1$