Complex Numbers And Quadratic Equations question 493

Question: If $ | z_1 |=| z_2 |=| z_3 |=1 $ and $ z_1+z_2+z_3=0 $ , If the area of the triangle whose vertices are $ z_1,z_2,z_3 $ is $ \sqrt{3}k $ , then find k.

Solution:

Answer: 0.75