(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There are three complex numbers a, b and c. Show that these propositions are equals.

1. ABC (triangle from the three points in complex plane) is equilateral (T_{1}).

2. j or j^{2}is the solution for az^{2}+ bz + c = 0.

3. a^{2}+ b^{2}+ c^{2}= ab + bc + ca

2. Relevant equations

There is a hint. Equilateral triangles made from the bases AB, BC, and CA have centres of gravity from which we can construct another equilateral triangle (T_{2}).

3. The attempt at a solution

T_{1}and T_{2}are equal triangles. They have the same heights and sides. I've tried to use the equation to solve quadratic equation (quadratic formula) and assumed j is a solution, hence j^{2}is compliment of j or [tex]\bar{j}[/tex]. I found ac-3b=1. I have no idea how to use the equation. Is my assumption correct? Or my approach to the question is wrong?

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# Homework Help: Complex numbers, plane and geometry

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