Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Imaginary volume

  1. Jan 30, 2015 #1
    Imaginary numbers enable one to envision a lot of ideas. But what kind of numbers/algebras would enable us to work with imaginary volumes? Volumes, by definition, always seem to be positive, since any cubes are. What kind of numbers would give/allow a more complex picture?
     
  2. jcsd
  3. Jan 31, 2015 #2

    Svein

    User Avatar
    Science Advisor

    The volumes you are familiar with exist in ℝ3. If you introduce imaginary numbers, the corresponding volumes would be in ℂ3. So a complex cube could be: Side "length": 1+ i. "Area": (1+i)*(1+i) = (1 + 2i + i2) = 2i. "Volume": (1+i)*(1+i)*(1+i) = 2i*(1+i) = -2+2i.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Imaginary volume
  1. Imaginary Numbers (Replies: 14)

  2. The imaginary Unit (Replies: 44)

Loading...