Let z1  and z2  be two roots of the equation z2+az+b=0, z  being complex. Further, assume that the origin, z1  and z2  form an equilateral triangle. Then

If z1, z2  and z3  are the vertices of an equilateral triangle. Then z12+z22+z32=z1z2+z2z3+z3z1 .∵     Origin, z1  and z2  are the vertices of an equilateral triangle, thenz12+z22=z1z2 ⇒  (z1+z2)2=3z1z2                            ….(i)Again z1, z2  are the roots of the equationz2+az+b=0 .Then z1+z2=−a  and z1z2=b Putting these values in Eq. (1), we have(−a)2=3b   ⇒ a2=3b