Let `lambda in R` . If the origin and the non-real roots of `2z^2+2z+lambda=0` form the three vertices of an equilateral triangle in the Argand plane, then `lambda` is (a.)`1` (b) `2/3` (c.) `2` (d.) `-1`

If z=omega,omega^2w h e r eomega is a non-real complex cube root of unity, are two vertices of an equilateral triangle in the Argand plane, then the third vertex z may be represented by (a) z=1 b. z=0 c. z=-2 d. z=-1

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot

Suppose z_(1),z_(2)andz_(3) are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z_(1)=1+isqrt3 then find z_(2)andz_(3) .

The roots of the equation t^3+3a t^2+3b t+c=0a r ez_1, z_2, z_3 which represent the vertices of an equilateral triangle. Then a^2=3b b. b^2=a c. a^2=b d. b^2=3a

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

Show that the area of the triangle on the Argand diagram formed by the complex number z ,i za n dz+i z is 1/2|z|^2

If z=(lambda+3)+isqrt(5-lambda^2) then the locus of Z is

If the equations 2x-lambday+5z=7 and lambda x-8y-10z+14=0 represent the same plane then lambda is :