If `|z_(1)|=|z_(2)|=|z_(3)|=1 and z_1+z_2+z_3=0` then the area of the triangle whose vertices are `z_1, z_2, z_3` is

Options

A. `3sqrt(3//4)`
B. `sqrt(3//4)`
C. 1
D. 2

Answer

A

Explanation

`|z_(1)|=|z_(2)|=|z_(3)|=1`
Hence, the cirumcenter of triangle is origin. Also, centroid `(z_(1)+z_(2)+z_(3))//3=0`, which coincides with the circumcentrer. So the triangle is equilateral . Since radius is 1, length of side is `a=sqrt(3)`. Therefore, the area of the triangle is `(sqrt3//4)a^(2)=(3sqrt3//4)`.