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Teaching myself trigconfusion

  1. Jul 27, 2005 #1
    Hi, I'm in the complex numbers section of a trig book, and I'm having trouble intuitively understanding how a number like 3+5i can become (3,5) on the Gaussian coordinate plane...the logic behind it doesn't jump out at me...

    Any help?

    And is calculus generally a smooth transition after mastering trig and algebra 2, or is it something totally different?

    Thanks a lot,
    Brady Yoon :redface:
     
  2. jcsd
  3. Jul 27, 2005 #2

    quasar987

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    ummm. The idea of the Gaussian plane is to represent complex numbers as vectors. We chose the x-axis to host the real part of the complex number and the y-axis to host the imaginary part. Thus a complex number a+bi has the vector representation (a,b) in the Gaussian plane.


    though you might not completely understand this, I will add that [itex]\mathbb{C}[/itex] and [itex]\mathbb{R}^2[/itex], as groups, are isomorphic to one another [according to the isomorphism that assigns to each complex number its corresponding vector in the Gaussian plane: f(a+bi) = (a,b)].
    Maybe someone else can extrapolate on what intesresting things this implies; I'd be interested. Thx.
     
    Last edited: Jul 27, 2005
  4. Jul 27, 2005 #3
    a smooth translation from trig is non existent. calculus is just alot of algebra with a few more formulas thrown in. dont let it scare you though, it isnt as hard as you think
     
  5. Jul 28, 2005 #4

    HallsofIvy

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    That's just a way of representing the complex numbers. Just as we can think of real numbers as numbers on a "number line", since every complex number, a+ bi, requires two real numbers, we need two number lines to represent complex number. It happens to be simplest to make those number lines perpendicular. The complex number a+bi is represented by the pair (a,b) in an obvious way and that corresponds to the point with coordinates (a, b).
     
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