For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is

The polar coordinate of a point P is $$\left( {2, - {\pi \over 4}} \right)$$. The polar coordinate of the point Q which is such that line joining PQ is bisected perpendicularly by the initial line, is

If $${Z_r} = \sin {{2\pi r} \over {11}} - i\cos {{2\pi r} \over {11}}$$, then $$\sum\limits_{r = 0}^{10} {{Z_r}} $$ is equal to

If z₁ and z₂ be two non-zero complex numbers such that $${{{z_1}} \over {{z_2}}} + {{{z_2}} \over {{z_1}}} = 1$$, then the origin and the points represented by z₁ and z₂