ABCD is a rhombus in the argand plane. If the affixes of the vertices are `z_1,z_2,z_3,z_4` respectively and `angle CBA=pi/3` then find the value of `z_1+omegaz_2+omega^2z_3` where omega is a complex cube root of the unity

ABCD is a rhombus in the argand plane.If the affixes of the vertices are z_(1),z_(2),z_(3),z_(4) respectively and /_CBA=(pi)/(3) then find the value of z_(1)+omega z_(2)+omega^(2)z_(3) where omega is a complex cube root of the unity

ABCD is a rhombus in the Argand plane. If the affixes of the vertices are z_(1),z_(2),z_(3) and z_(4) respectively, and angleCBA=pi//3 , then

ABCD is a rhombus in the Argand plane. If the affixes of the vertices are z_(1),z_(2),z_(3) and z_(4) respectively, and angleCBA=pi//3 , then

ABCD is a rhombus in the Argand plane.If the affixes of the vertices be z_(1),z_(2),z_(3),z_(4) and taken in anti-clockwise sense and /_CBA=(pi)/(3), show that

If |z|=3 , then area of the triangle whose sides are z , omegaz and z +omegaz (where omega is a complex cube root of unity) is

If z^(2)(bar(omega))^(4)=1 where omega is a nonreal complex cube root of 1 then find z .

If |z| = 3, the area of the triangle whose sides are z, omega z and z + omega z (where omega is a complex cube root of unity) is

If |z| =3 , the area of the triangle whose sides are z , omega z and z + omega z (where omega is a complex cube root of unity) is

If z is a complex number satisfying |z-3|<=4 and | omega z-1-omega^(2)|=a (where omega is complex cube root of unity then

If the are of the triangle formed by z,omega z and z+omega z where omega is cube root of unity is 16sqrt(3) then |z|=?