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Algebra 101, and some about complex numbers

  1. Sep 6, 2008 #1
    1. The problem statement, all variables and given/known data
    I was looking up complex numbers and the guy on YouTube made something similar to this equation:
    i=-1
    c^2-(d^2*i^2) = c^2+d^2

    ( - 2:55)

    2. Relevant equations
    I do not understand why it is "c^2+d^2" and not "c^2-d^2"
    I would like a detailed explanation, as I might have misunderstood algebra somehow

    3. The attempt at a solution
    I would do this to find a solution
    c^2-(d^2*i^2)
    c^2-(d^2*(-1)^2)
    c^2-(d^2*1)
    c^2-d^2
     
    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Sep 6, 2008 #2
    The general form of a complex nr is ;a+bi, where i is the imaginary.

    it is the square root of negative one, that is:

    [tex]\sqrt{-1}=i=>i^2=-1[/tex] now going back to what u have there

    [tex]c^2-(d^2i^2)=c^2-(d^2(-1))=c^2+d^2[/tex]
     
  4. Sep 6, 2008 #3
    I see, so my problem wasn't with algebra but with my understanding of complex numbers.
    Then it makes perfect sense! I thank you good sir =P
     
  5. Sep 6, 2008 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Here was your error. i is NOT -1. Its square is -1: i2= -1.

     
    Last edited by a moderator: Sep 25, 2014
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