What is the square root of $i$, where $i=\sqrt{-1}$?

$\left(x^3-1\right)$ can be factorised as, where, $\omega$ is one of the cube roots of unity.

If $z_1$ and $z_2$ are complex numbers with $\left|z_1\right|=\left|z_2\right|$, then which of the following is/are correct?

I. $z_1=z_2$

II. Real part of $z_1=$ Real part of $z_2$

III. Imaginary part of $z_1=$ Imaginary part of $z_2$

Select the correct answer using the code given below