The incentre of the triangle with vertices $$\left( {1,\,\sqrt 3 } \right),\left( {0,\,0} \right)$$ and $$\left( {2,\,0} \right)$$ is

If $$\arg \left( z \right) < 0,$$ then $$\arg \left( { - z} \right) - \arg \left( z \right) = $$

If $${z_1},\,{z_2}$$ and $${z_3}$$ are complex numbers such that $$\left| {{z_1}} \right| = \left| {{z_2}} \right| = \left| {{z_3}} \right| = \left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right| = 1,$$ then $$\left| {{z_1} + {z_2} + {z_3}} \right|$$ is

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation