Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$

If $$P=(1, 0),$$ $$Q=(-1, 0)$$ and $$R=(2, 0)$$ are three given points, then locus of the point $$S$$ satisfying the relation $$S{Q^2} + S{R^2} = 2S{P^2},$$ is

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

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

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