Imaginary volume

  • Thread starter samsara15
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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?
 

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Svein
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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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