Question

If $i{z}^3+z^2-z+i=0$, then $|z|$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

Answer: (B)

$1$

Given : $i{z}^3+z^2-z+i=0$
Dividing both sides by $i$ and using $\frac{1}{i}=-i$.
We have,
$z^3-i{z}^2+iz+1=0$
$\Rightarrow z^2(z-i)+i(z-i)=0$ ...... $(\because i^2=-1)$
$\Rightarrow (z-i)(z^2+i)=0$
$\therefore z=i$ or $z^2=-i$
$\therefore |z|=|i|=1$
and $|z{|}^2=|z^2|=|-i|=1$
$\therefore |z|=1$.