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.`

If the complex number A(z_(1)),B(z_(2)) and origin forms an isosceles triangle such that angle(AOB) = (2pi)/3 ,then (z_(1)^(2)+z_(2)^(2) +4z_(1)z_(2))/(z_(1)z_(2)) equals ________

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 .

The complex numbers z_(1), z_(2) and the origin are the vertices of an equilateral triangle in the Argand plane Prove that z_(1)^(2)+ z_(2)^(2)= z_(1).z_(2)

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If z_(1),z_(2) are vertices of an equilateral triangle with z_(0) its centroid, then z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=

Consider the complex numbers z_(1) and z_(2) Satisfying the relation |z_(1)+z_(2)|^(2)=|z_(1)|^2 + |z_(2)|^(2) Complex number z_(1)/z_(2) is

Find the condition in order that z_(1),z_(2),z_(3) are vertices of an.isosceles triangle right angled at z_(2) .

If z_(1),z_(2), z_(3) are vertices of an equilateral triangle with z_(0) its centroid, then z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=

If z_1 , z_2 ,z_3 are the vertices of an isosceles triangle right angled at z_2 , then prove that (z_1)^2+2(z_2)^2+(z_3)^2=2(z1+z3)z2

Consider the complex numbers z_(1) and z_(2) Satisfying the relation |z_(1)+z_(2)|^(2)=|z_(1)| + |z_(2)|^(2) Complex number z_(1)//z_(2) is