The area of the triangle with vertices A(z), B(iz) and C(z + iz) is :

The least value of |z| where z is complex number which satisfies the inequality $$\exp \left( {{{(|z| + 3)(|z| - 1)} \over {||z| + 1|}}{{\log }_e}2} \right) \ge {\log _{\sqrt 2 }}|5\sqrt 7 + 9i|,i = \sqrt { - 1} $$, is equal to :

Let a complex number z, |z| $$\ne$$ 1,

satisfy $${\log _{{1 \over {\sqrt 2 }}}}\left( {{{|z| + 11} \over {{{(|z| - 1)}^2}}}} \right) \le 2$$. Then, the largest value of |z| is equal to ____________.

If $$\alpha$$, $$\beta$$ $$\in$$ R are such that 1 $$-$$ 2i (here i² = $$-$$1) is a root of z² + $$\alpha$$z + $$\beta$$ = 0, then ($$\alpha$$ $$-$$ $$\beta$$) is equal to :