Let $$z$$ be a complex number such that $$|z|+z=3+i, i=\sqrt{-1}$$, then $$|z|$$ is equal to

If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y =

The sqaure roots of the complex number $$(-5-12 \mathrm{i})$$ are

If amplitude of $$(z-2-3 i)$$ is $$\frac{3 \pi}{4}$$, then locus of $$z$$ is (where $$z=x+i y$$)