The value of $${i^{2n}} + {i^{2n + 1}} + {i^{2n + 2}} + {i^{2n + 3}}$$, where $$i = \sqrt { - 1} $$, is

The value of $${\left( {{{ - 1 + i\sqrt 3 } \over 2}} \right)^n} + {\left( {{{ - 1 - i\sqrt 3 } \over 2}} \right)^n}$$, where n is not a multiple of 3 and $$i = \sqrt { - 1} $$, is

If 1, $$\omega$$, $$\omega$$² are the cube roots of unity, then (1 + $$\omega$$)(1 + $$\omega$$²)(1 + $$\omega$$³)(1 + $$\omega$$ + $$\omega$$²) is equal to

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