Which of the following are correct for any two complex numbers $z_1$ and $z_2$?

If $P, Q$ and $R$ are angles of an isosceles triangle and $\angle P = \frac{\pi}{2}$,then the value of $\left(\cos \frac{P}{3} - i \sin \frac{P}{3}\right)^3 + (\cos Q + i \sin Q) (\cos R - i \sin R) + (\cos P - i \sin P) (\cos Q - i \sin Q) (\cos R - i \sin R)$ is:

If $(1 + i)(1 + 2i)(1 + 3i) \dots (1 + ni) = a + ib$,then $2 \times 5 \times 10 \times \dots \times (1 + n^2)$ is equal to

If $z = x + iy$ and $x^2 + y^2 = 1$,then $\frac{1 + x + iy}{1 + x - iy} = $

Find the maximum value of $|z|$ when $\left|z-\frac{3}{z}\right|=2,$ where $z$ is a complex number.

The value of $\sum_{n=0}^{\infty}\left(\frac{2 i}{3}\right)^n$ is