If z is any complex number and $$\text{Given: } iz^3 + z^2 - z + i = 0, \text{ where } i = \sqrt{-1}, \quad$$then what is the value of $$\text{Find: } (|z| + 1)^2$$ ?

Correct option is B

​$$\text{Given: } iz^3 + z^2 - z + i = 0, \text{ where } i = \sqrt{-1}, \quad$$​

Solution:

$$\begin{aligned}&iz^3 + z^2 - z + i = 0 \\&iz^2(z - i) - 1(z - i) = 0 \\&(iz^2 - 1)(z - i) = 0 \\&z^2 = \frac{1}{i}, \quad (z = i) \\&|z| = 1 \\&(|z| + 1)^2 = (1 + 1)^2 = 4\end{aligned}$$​