The smallest positive integral value of n such that $${\left[ {{{1 + \sin {\pi \over 8} + i\cos {\pi \over 8}} \over {1 + \sin {\pi \over 8} - i\cos {\pi \over 8}}}} \right]^n}$$ is purely imaginary, is equal to

If Re(z + 2) = | z $$-$$ 2 |, then the locus of z is