The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :

If the four complex numbers $$z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$$ and $$z-2Re(z)$$ represent the vertices of a square of side 4 units in the Argand plane, then $$|z|$$ is equal to :

If a and b are real numbers such that
$${\left( {2 + \alpha } \right)^4} = a + b\alpha $$
where $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$ then a + b is equal to :

Let $$u = {{2z + i} \over {z - ki}}$$, z = x + iy and k > 0. If the curve represented
by Re(u) + Im(u) = 1 intersects the y-axis at the points P and Q where PQ = 5, then the value of k is :