Question

If $i{z}^3+z^2-z+i=0$, then find the value of $\left|z\right|$

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is A $1$

$giventhat,i{z}^3+z^2-z+i=0now,{iz}^2(z-i)-(z-i)=0(z-i)\{i{z}^2-1\}=0z-i=0z=i\left|z\right|=\left|i\right|=1ori{z}^2-1=0z^2=-iz=\pm \sqrt{-i}\left|z\right|=\left|\sqrt{-i}\right|=1$