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.

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

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

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

z_(1) and z_(2) are two non-zero complex numbers such that z_(1)^(2)+z_(1)z_(2)+z_(2)^(2)=0 . Prove that the ponts z_(1),z_(2) and the origin form an isosceles triangle in the complex plane.

Let z_(1)" and "z_(2) be the roots of the equation z^(2)+pz+q=0 , where p,q are real. The points represented by z_(1),z_(2) and the origin form an equilateral triangle if

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.

If theta is real and z_1, z_2 are connected by z_1 2+z_2 2+2z_1z_2costheta=0, then prove that the triangle formed by vertices O ,z_1a n dz_2 is isosceles.

If theta is real and z_1, z_2 are connected by z1 2+z2 2+2z_1z_2costheta=0, then prove that the triangle formed by vertices O ,z_1a n dz_2 is isosceles.

If theta is real and z_1, z_2 are connected by z1 2+z2 2+2z_1z_2costheta=0, then prove that the triangle formed by vertices O ,z_1a n dz_2 is isosceles.