If $x = 3 - 2\sqrt{3}i$,then $x^4 - 12x^3 + 54x^2 - 108x - 54 = $

If $x_n = \cos \left(\frac{\pi}{4^n}\right) + i \sin \left(\frac{\pi}{4^n}\right)$,then the product $x_1 x_2 x_3 \ldots \infty$ is equal to

If $z \in \mathbb{C}$,then the minimum value of $|z| + |2z - 3| + |z - 1|$ is

If $(x-iy)^{1/3} = a-ib$,then the value of $\frac{x}{a} + \frac{y}{b}$ is

The sum of all possible values of $\theta \in[-\pi, 2 \pi]$, for which $\frac{1+i \cos \theta}{1-2 i \cos \theta}$ is purely imaginary, is equal to (in $\pi$)

If $z = x + iy$ is a complex number such that $z\bar{z}^3 + \bar{z}z^3 = 350$ and $x, y$ are integers,then $|z| = $