If $$\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2$$, where $$z_1$$ and $$z_2$$ are two complex numbers, then

A real value of $$x$$ will satisfy the equation, $$\left(\frac{3-4 i x}{3+4 i x}\right)=\alpha-i \beta,(\alpha, \beta$$ are real $$)$$, if

What is the value of $$(1-i \sqrt{3})^9$$ is equal to

$$\left(\frac{\sqrt{6}-\sqrt{2}}{4}+\frac{\sqrt{6}+\sqrt{2}}{4} i\right)^{2020}$$ is equal to