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Simple complex analysis question

  1. Aug 18, 2011 #1
    Hi,

    In complex analysis, is it an axiom that iy=yi where y is real? Or can this result be proved somehow? Thank you.
     
  2. jcsd
  3. Aug 18, 2011 #2

    micromass

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    Well, it depends on how you define the product. The most elementary way to define complex numbers is by defining the to be couples (a,b) with addition

    (a,b)+(c,d)=(a+c,b+d)
    (a,b)(c,d)=(ac-bd,bc+ad)

    Here a real number is of the form (a,0) and i is (0,1). It can now easily be checked tht

    (a,0)(0,1)=(0,a)=(0,1)(a,0).
     
  4. Aug 18, 2011 #3
    Thank you micromass. That is a nice way of looking at it
     
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