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

The conjugate of the complex number $${{{{(1 + i)}^2}} \over {1 - i}}$$ is

The imaginary part of $$i^i$$ is

The amplitude of $${(1 + i)^5}$$ is