The modulus and principal argument of the complex number $${{1 + 2i} \over {1 - {{(1 - i)}^2}}}$$ are

If $$\left| {z + 4} \right| \le 3$$, then the maximum value of $$\left| {z + 1} \right|$$ is

The number of roots of the equation $${z^2} = 2\overline z $$ is

What is the value of $${\left( {{{ - 1 + i\sqrt 3 } \over 2}} \right)^{3n}} + {\left( {{{ - 1 - i\sqrt 3 } \over 2}} \right)^{3n}}$$, where $$i = \sqrt { - 1} $$?