If  $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=1$ and  $z_1+z_2+z_3=0$, then area of the triangle with vertices  $z_1,z_2$ and $z_3$  is

$\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=1$

$\Rightarrow$circum – centre of the triangle is origin
Also,  $\frac{z_1+z_2+z_3}{3}=0$
Centroid is origin
So, triangle is equilateral
Since, radius =1, length of side is  $a=\sqrt{3}$
Area of $\Delta =\frac{\sqrt{3}}{4}\times {\left(a\right)}^2=3\frac{\sqrt{3}}{4}$