$$ \text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is } $$

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

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