If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals :

The number of complex numbers z such that $$\left| {z - 1} \right| = \left| {z + 1} \right| = \left| {z - i} \right|$$ equals :

If $$\,\left| {z - {4 \over z}} \right| = 2,$$ then the maximum value of $$\,\left| z \right|$$ is equal to :

The conjugate of a complex number is $${1 \over {i - 1}}$$ then that complex number is :