If $z_1$ and $z_2$ are any two complex numbers,then $|z_1 + \sqrt{z_1^2 - z_2^2}| + |z_1 - \sqrt{z_1^2 - z_2^2}|$ is equal to

If $Z_1$ and $Z_2$ are two non-zero complex numbers,then which of the following is not true?

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:

If $a, b \in \mathbb{R}$ and $i=\sqrt{-1}$,then the number of ordered pairs of real numbers $(a, b)$ satisfying the condition $(a+bi)^3 = a-bi$ is

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

The $A + iB$ form of $\frac{(\cos x + i\sin x)(\cos y + i\sin y)}{(\cot u + i)(1 + i\tan v)}$ is