If |Z₁ |= |Z₂ |= |Z₃ |=1 and Z₁+Z₂+Z₃=0 , then the area of the triangle whose vertices are Z₁, Z₂, Z₃ is

Step-by-step solution

Given: - ( |Z₁ |= |Z₂ |= |Z₃ |=1 ) - (Z₁+Z₂+Z₃=0 ) Concept: If three complex numbers lie on the unit circle and their sum is zero, they form an equilateral triangle on the Argand plane. For equilateral triangle with side (a=1 ), the area is: ( Area = 3 4 a^2= 3 4 (1)^2= 3 4 ) But since all sides are of length 1 on the unit circle, and the centroid (origin) divides the medians in 2:1, the full triangle formed by 3 such points has area: ( 3 3 4 )