If $z = \frac{7 - i}{3 - 4i}$,then $z^{14} = $

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 $\frac{2z_1}{3z_2}$ is a purely imaginary number,then $\left| \frac{z_1 - z_2}{z_1 + z_2} \right| =$

If $z_1$ and $z_2$ are complex numbers such that $\frac{2 z_1}{3 z_2}$ is a purely imaginary number, then the value of $\left|\frac{z_1-z_2}{z_1+z_2}\right|$ is

If $z=x+iy$ and $z^{1/3}=p+iq$,where $x, y, p, q \in R$ and $i=\sqrt{-1}$,then the value of $\left(\frac{x}{p}+\frac{y}{q}\right)$ is

If $z_1$ and $z_2$ are two unimodular complex numbers that satisfy $z_1^2 + z_2^2 = 5,$ then $(z_1 - \bar{z}_1)^2 + (z_2 - \bar{z}_2)^2$ is equal to -