Double imaginary numbers | Mathematics | Page 1

rain pagoda Jun 25, 2024, 3:42 PM

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Are there double imaginary numbers? Maybe j=sqrt(-i)?

oak acornBOT Jun 25, 2024, 3:42 PM

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junior flax Jun 25, 2024, 4:06 PM

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there's already solutions to z^2 = -i in the complex numbers, you'd be adding nothing

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there's stuff like the quaternions if you want more imaginary axes

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https://en.wikipedia.org/wiki/Quaternion

Quaternion

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold by

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@rain pagoda

rain pagoda Jun 25, 2024, 4:46 PM

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Ok but do you have "map" like this but with only i and j? (Or i and k)
@junior flax

junior flax Jun 25, 2024, 5:06 PM

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there is no "3d complex" numbers if that's what you're asking @rain pagoda

rain pagoda Jun 25, 2024, 5:06 PM

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Sad

junior flax Jun 25, 2024, 5:07 PM

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(at least not without breaking some nice properties, namely all "3d complex" numbers having inverses)

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this mathoverflow answer might be interesting https://math.stackexchange.com/a/1784336

Mathematics Stack Exchange

Why are There No "Triernions" (3-dimensional analogue of complex nu...

Since there are complex numbers (2 dimensions) and quaternions (4 dimensions), it follows intuitively that there ought to be something in between for 3 dimensions ("triernions").

Yet no one uses...

rain pagoda Jun 25, 2024, 5:07 PM

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So how i can make munelbulb?

junior flax Jun 25, 2024, 5:07 PM

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wym?

rain pagoda Jun 25, 2024, 5:08 PM

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3d mandelbort set

junior flax Jun 25, 2024, 5:14 PM

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well there's no natural generalization in 3d of the mandelbrot set yeah

#Double imaginary numbers