- #1
lolittaFarhat
- 7
- 0
z1,z2,z3 are distinct complex numbers, prove that they are the vertices of an equilateral triangle if and only if the following relation is satisfied:
z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1
so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.
z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1
so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.
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