1. Not finding help here? Sign up for a free 30min 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!

A complex problem

  1. Nov 26, 2006 #1
    it's ic a problem on comlex numbers
    IF z1 ,z2 ,z3 are vertices of equilateral triangle in argand plane
    then
    P.T.
    z1*z1 + z2*z2 =z1*z2
    i hav 1 soln but it's not tat satisfactory :confused:
     
  2. jcsd
  3. Nov 26, 2006 #2

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    Why doesn't z3 appear anywhere in the equation you're trying to prove?
     
  4. Nov 27, 2006 #3
    cos we hav to eliminate z3
     
  5. Nov 27, 2006 #4

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    No, it's because either you wrote the question wrong or the question given to you was stated wrong. What you've asked to prove is impossible to prove, because it's false in general.
     
  6. Nov 27, 2006 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    One example would be to take the vertices of the equilateral triangle to be the cube roots of 1: 1, [itex]-\frac{1}{2}+i\frac{\sqrt{3}}{2}[/itex], and [itex]-\frac{1}{2}-i\frac{\sqrt{3}}{2}[/itex]. If we take z1= 1, z2= [itex]-\frac{1}{2}+i\frac{\sqrt{3}}{2}[/itex], then z12+ z22= [itex]\frac{1}{2}-i\frac{\sqrt{3}}{2}[/itex] which is not z1z2!

    Go back and check exactly what it is you are asked to prove.
     
  7. Nov 27, 2006 #6

    AKG

    User Avatar
    Science Advisor
    Homework Helper

    Or take z1 = 0, z2 = anything else, and z3 any of the two points in the plane that would make z1, z2, z3 an equilateral triangle.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A complex problem
  1. Complex numbers' problem (Replies: 20)

Loading...