If $$S = \left\{ {z \in C:{{z - i} \over {z + 2i}} \in R} \right\}$$, then :

If $${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$$, then p and q are roots of the equation :

The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :

Let C be the set of all complex numbers. Let

S₁ = {z$$\in$$C : |z $$-$$ 2| $$\le$$ 1} and

S₂ = {z$$\in$$C : z(1 + i) + $$\overline z $$(1 $$-$$ i) $$\ge$$ 4}.

Then, the maximum value of $${\left| {z - {5 \over 2}} \right|^2}$$ for z$$\in$$S₁ $$\cap$$ S₂ is equal to :