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Homework Help: Complex numbers, plane and geometry

  1. Feb 16, 2010 #1
    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 (T1).
    2. j or j2 is the solution for az2 + bz + c = 0.
    3. a2 + b2 + c2 = 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 (T2).


    3. The attempt at a solution
    T1 and T2 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 j2 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?
     
    Last edited: Feb 16, 2010
  2. jcsd
  3. Feb 16, 2010 #2

    HallsofIvy

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    Is this an engineering class? That is, is "j" the imaginary unit, j2= -1?
     
  4. Feb 16, 2010 #3
    This is a mathematic class and we use i as the imaginary unit. I don't think that the teacher mistyped it.
     
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