Question:
If complex numbers z₁,z₂,z₃ are vertices of an equilateral triangle, then
z₁²+z₂²+z₃²-z₁z₂-z₂z₃-z₃z₁ is equal to
If complex numbers z₁,z₂,z₃ are vertices of an equilateral triangle, then
z₁²+z₂²+z₃²-z₁z₂-z₂z₃-z₃z₁ is equal to
Show Hint
Use symmetry properties for equilateral triangle problems.
Updated On: Mar 20, 2026
- \(0\)
- \(z_1-z_2\)
- \(z_1+z_2\)
- 1
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The Correct Option is A
Solution and Explanation
For vertices of an equilateral triangle, the symmetric expression
z₁²+z₂²+z₃²-z₁z₂-z₂z₃-z₃z₁=0
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