$${(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}$$ is equal to

What is the argument of the complex number $${{(1 + i)(2 + i)} \over {3 - i}}$$, where $$i = \sqrt { - 1} $$ ?

Evaluate $${\left[ {{i^{18}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}$$.

If $${(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)$$, then $${a^2} + {b^2}$$ is equal to