Question

Prove that if z1 +z2 +z3 =0 and |z1|=|z2|=|z3| =1, then this points are the vertices of an equilateral triangle inscribed in the unit circle |z|=1

Answer 1

but i don't think that circle of radius will be 1

Answer 2

thats what book says

Answer 3

this will be an equilateral triangle .. for sure, since all vertices are equal and summation zero implies it's a triangle ... but inscribed in circle of unit radius??