8. If `z_1^2+z_2^2+2z_.z_2.costheta= 0 ` prove that the points represented by `z_1, z_2`, and the origin form an isosceles triangle.

8.If z_(1)^(2)+z_(2)^(2)+2zz_(2)*cos theta=0 prove that the points represented by z_(1),z_(2), and the origin form an isosceles triangle.

Let z_1 and z_2 be the roots of z^2+pz+q =0. Then the points represented by z_1,z_2 the origin form an equilateral triangle if p^2 =3q.

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.

If theta is real and z_(1),z_(2) are connected by z_(1)^(2)+z_(2)^(2)+2z_(1)z_(2)cos theta=0, then prove that the triangle formed by vertices O,z_(1)andz_(2) is isosceles.

Prove that the complex numbers z_1 and z_2 and the origin form an isosceles triangle with vertical angle 2pi//3" if " z_1^2+z_2^2+z_1z_2=0

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

Prove that the complex numbers z_(1) and z_(2) and the origin form an isosceles triangle with vertical angle (2pi)/(3),ifz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0.