Home › JEE Advanced › Mathematics › Complex Numbers › If z1, z2, z3 are vertices of an equilateral tri…
If z1, z2, z3 are vertices of an equilateral triangle, then:
Az1² + z2² + z3² = z1 z2 + z2 z3 + z3 z1
Bz1 = z2 = z3
CBoth might hold
Dz1 + z2 + z3 = 0
Answer & Solution
Correct answer: A. z1² + z2² + z3² = z1 z2 + z2 z3 + z3 z1
For equilateral triangle, the condition z1² + z2² + z3² = z1z2 + z2z3 + z3z1 holds (equivalently |z1 - z2| = |z2 - z3| = |z3 - z1|). Sum z1+z2+z3 = 0 only when centroid is origin (a special case).
Related questions
Using De Moivre's theorem, the complex roots of $z^3=1$ are:If $\alpha$ and $\beta$ are roots of $z^2+4z+8=0$, then $\dfrac{\alpha+\beta+4i}{\alpha\beThe locus $\left|\dfrac{z-2}{z+3i}\right|=4$ simplifies to which equation?Simplify i raised to the power 27. What is the result?Multiply (2 + 3i) by (4 - i). What is the product in standard form?How is the complex conjugate of a complex number obtained?Add the complex numbers 5 - 2i and 3 + 7i. What is the sum?In the complex number 7 + 4i, which part is the real part?