If $$z = {4 \over {1 - i}}$$, then $$\overline z $$ is (where $$\overline z $$ is complex conjugate of z)

If $$ - \pi < \arg (z) < - {\pi \over 2}$$, then $$\arg \overline z - \arg ( - \overline z )$$ is

For the real parameter t, the locus of the complex number $$z = (1 - {t^2}) + i\sqrt {1 + {t^2}} $$ in the complex plane is

If $$x + {1 \over x} = 2\cos \theta $$, then for any integer n, $${x^n} + {1 \over {{x^n}}} = $$