Let $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1}$$ $$ \ne $$ $${z_2}$$ and $$\left| {{z_1}} \right| =\,\left| {{z_2}} \right|$$. If $${z_1}$$ has positive real and $${z_2}$$ has negative imaginary part, then $${{{z_1}\, + \,{z_2}} \over {{z_1}\, - \,{z_2}}}$$ may be

The expression $$2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \right)} \right]$$ is equal to

Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is $${1 \over 2}\,{\left| z \right|^2}$$ .

If $$S$$ is the set of all real $$x$$ such that $${{2x - 1} \over {2{x^3} + 3{x^2} + x}}$$ is positive, then $$S$$ contains