If i z 3 + z 2 - z + i = 0 (where z is a complex number), then the value of z is

$i{z}^3+z^2-z+i=0 \Rightarrow i{z}^2\left(z-i\right)-\left(z-i\right)=0$

$\Rightarrow \left(z-i\right) \left(i{z}^2-1\right)=0$

Either $z=i$  $\Rightarrow \left|z\right|=1$

or

$\Rightarrow i{z}^2=1 ....\left(1\right)$

$\Rightarrow -i {\overline{z}}^2=1 ....\left(2\right)$

Multiplying equation $\left(1\right)$ & $\left(2\right)$

${\left(z \overline{z}\right)}^2=1 \Rightarrow \left|z\right|=1$