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

If $${a_r} = {(\cos 2r\pi + i\sin 2r\pi )^{1/9}}$$,

then the value of $$\left| {\matrix{ {{a_1}} & {{a_2}} & {{a_3}} \cr {{a_4}} & {{a_5}} & {{a_6}} \cr {{a_7}} & {{a_8}} & {{a_9}} \cr } } \right|$$ is equal to

Let z₁ and z₂ be complex numbers such that z₁ $$ \ne $$ z₂ and |z₁| = |z₂|. If Re(z₁) > 0 and Im(z₂) < 0, then $${{{z_1} + {z_2}} \over {{z_1} - {z_2}}}$$ is