1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook