Solving a complex geometry problem Given three complex numbers Z1, Z2 and Z3, if Z1 ^ 2 + Z2 ^ 2 + Z3 ^ 2-z1z2-z1z3-z2z3 = 0, it is proved that the triangle with Z1, Z2 and Z3 as vertices is regular triangle

Solving a complex geometry problem Given three complex numbers Z1, Z2 and Z3, if Z1 ^ 2 + Z2 ^ 2 + Z3 ^ 2-z1z2-z1z3-z2z3 = 0, it is proved that the triangle with Z1, Z2 and Z3 as vertices is regular triangle

Z1 ^ 2 + Z2 ^ 2 + Z3 ^ 2-z1z2-z1z3-z2z3 = 0 is equivalent to (z2-z1) ^ 2 - (z2-z1) (z3-z1) + (z3-z1) ^ 2 = 0. It can be solved that z2-z1 = (1 + sqrt (3) I) / 2 * (z3-z1), or z2-z1 = (1-sqrt (3) I) / 2 * (z3-z1)

Elden Ring Premiere

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