$$ \text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is } $$

If $$z=\sqrt{3}+i$$, then the argument of $$z^2 e^{z-i}$$ is equal to

If $$i=\sqrt{-1}$$ and $$n$$ is a positive integer, then $$i^n+i^{n+1}+i^{n+2}+i^{n+3}$$ is equal to

If $$\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)$$, where $$x$$ and $$y$$ are real, then the ordered pair $$(2 x, 2 y)$$ is