[" 4.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 with ve "],[" equilateral."]

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.

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.

z_(1)bar(z)_(2)+bar(z)_(1)z_(2)=2|z_(1)||z_(2)|cos(theta_(1)-theta_(2))

Prove that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)=2|z_(1)|^(2) + 2|z_(2)|^(2)

If |z|=2 and the locus of 5z-1 is the circle having radius 'a' and z_(1)^(2)+z_(2)^(2)-2z_(1)z_(2)cos theta=0 then |z_(1)|:|z_(2)|=

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.

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .