1. Limited time only! Sign up for a free 30min personal 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!

Imaginary into real but not vice versa?

  1. Jun 3, 2009 #1
    Its kinda weird (atleast to me) that we can convert imaginary numbers into real, there is just a simple procedure/function called multiplication. You multiply two no. and you get a real ,though negative. But not to worry we can still multiply it with 2 [tex]i's[/tex] or say [tex]i^2[/tex]. To make it positive.
    But what about real numbers?
    There is no such operation. Yeah, we can surely say that
    [tex]2 =\frac{\ 2i}{i}[/tex] but this is not a satisfactory answer.
    So why is there a way to imaginary to rela but not vice versa?
  2. jcsd
  3. Jun 4, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Quite simply because fewer laws/restrictions constitute the definition of the complex numbers than the reals, and that all the laws valid for complex numbers are valid for the reals as well.
    That is, the reals can be regarded as a subset of the complex numbers, and "producible" from other complex numbers through an operation like multiplication.

    Fully analogous is the case with rationals viz. integers with respect to the operation of multiplication:

    It is impossible to multiply two integers and get a non-integer fraction, but 3/2*2/3, for example, equals the integer 2.
  4. Jun 4, 2009 #3


    User Avatar
    Science Advisor

    The real numbers are "closed" under the usual arithmetic operations. The complex numbers are also but include the real numbers as a subset.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook