Let `z_1, z_2, z_3` be the three nonzero complex numbers such that `z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot` Let `|a b c b c a c a b|=0` `a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2` orthocentre of triangle formed by `z_1, z_2, z_3, i sz_1+z_2+z_3` if triangle formed by `z_1, z_2, z_3` is equilateral, then its area is `(3sqrt(3))/2|z_1|^2` if triangle formed by `z_1, z_2, z_3` is equilateral, then `z_1+z_2+z_3=0`