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B Imaginary number dimensions

  1. Mar 31, 2016 #1
    Complex numbers ##a+bi## can be thought of as a second dimension extension of the real number line.

    Is there a third dimension version of this? Are there even more complex numbers that not only extend into the y axis but also the z axis?

    tex
     
  2. jcsd
  3. Mar 31, 2016 #2

    PeroK

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    Not 3, but 4 dimensions:

    https://en.wikipedia.org/wiki/Quaternion
     
  4. Mar 31, 2016 #3

    Ssnow

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    yes, You can obtain it considering ##\mathbb{C}\times \mathbb{R}## as structure space and giving rules for the addition and multiplication, from the history point of view is not used so much this extension ...
    More interesting is the ##4## dimensional extension, this is the set of quaternions ...
     
    Last edited: Mar 31, 2016
  5. Mar 31, 2016 #4

    Mark44

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    Fixed that for you...
     
  6. Apr 1, 2016 #5
    So is it correct to say that the single dimension real numbers can be considered a subset of the two dimensional complex number set where the real numbers are complex numbers with a 0 imaginary component?

    tex
     
  7. Apr 1, 2016 #6

    PeroK

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    Yes!
     
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