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Homework Statement
Let {z1,z2,z3} be complex variables such that |z1| = |z2| = |z3|. Prove that z1,z2,z3 are vertices of an equilateral triangle iff z1 + z2 + z3 = 0.
Homework Equations
The Attempt at a Solution
Not really sure where to start on this. I know that |z2-z1= |z3-z2| = |z3-z1|, but this information didn't get me very far. Any hints on how I should start this proof, or what other information I will need?