Sum of the first n terms of the series $${1 \over 2} + {3 \over 4} + {7 \over 8} + {{15} \over {16}} + ............$$ is equal to

The value of the expression $$\sqrt 3 \,\cos \,ec\,{20^0} - \sec \,{20^0}$$ is equal to

The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle.

For any two complex numbers $${z_1},{z_2}$$ and any real number a and b.

$$\,{\left| {a{z_1} - b{z_2}} \right|^2} + {\left| {b{z_1} + a{z_2}} \right|^2} = .........$$