The complex numbers `z_1, z_2` and the origin form an equilateral triangle only if (A) `z_1^2+z_2^2-z_1z_2=0` (B) `z_1+z_2=z_1z_2` (C) `z_1^2-z_2^2=z_1z_2` (D) none of these

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 a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n z_1+z_2=0 b. z_1z_2=1 c. z_1=z _2 d. none of these

If z_1,z_2,z_3 be the vertices of an equilateral triangle, show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)= 0 or z_1^2+z_2^2+z_3^2= z_1z_2+z_2z_3+z_3z_1 .

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 numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

Complex numbers z_(1),z_(2),z_(3) are the vertices of A,B,C respectively of an equilteral triangle. Show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=-2,z_3=1-isqrt(3)

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 ________

If z_1,z_2,z_3 are non zero non collinear complex number such that 2/z_1=1/z_2+ 1/z_3, then (A) ponts z_1,z_2,z_3 form and equilateral triangle (B) points z_1,z_2,z_3 lies on a circle (C) z_1,z_2,z_3 and origin are concylic (D) z_1+z_2+z_3=0