If $i z^{3}+z^{2}-z+i=0$ then show that $|z|$=___

Question

Professor PC Thomas Classes · Answer

$i z^{3}+z^{2}-z+i=0$\ $\Rightarrow(z-i)\left(i z^{2}-1ight)=0 \Rightarrow(z-i) i\left(z^{2}+iight)=0$\ $\Rightarrow \quad(z-i)=0$ or $z^{2}=-i$\ $\Rightarrow \quad|z|=|i|$ or $|z|^{2}=|-i|$\ In any case $|z|=1$.\