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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


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    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.
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