If $\sqrt{-3-4 i}=re^{i \theta}$,then $r^2 \tan \theta=$

$z = \frac{3 + 2i \sin \theta}{1 - 2i \sin \theta}, \quad (i = \sqrt{-1})$ will be purely imaginary if $\theta =$

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

Assertion $(A)$: If $z$ is a complex number such that $|z| \geq 3$,then the least value of $|z + \frac{3}{z}|$ is $1$.
Reason $(R)$: $|z_1 - z_2| \leq |z_1| + |z_2|$,for any two complex numbers $z_1, z_2$.
The correct option among the following is:

Let the complex numbers $\alpha$ and $\frac{1}{\bar{\alpha}}$ lie on the circles $|z-z_0|^2=4$ and $|z-z_0|^2=16$ respectively,where $z_0=1+i$. Then,the value of $100|\alpha|^2$ is.

If $x = 1 + 2i$,then the value of $x^3 + 7x^2 - x + 16$ is