Can imaginary numbers coexist on the same two dimensional space as real numbers?
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royal77 says hello friend
ANSWERS: 5
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i imagine they can.
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Yes. On a 2d Argand diagram, the real numbers form the x axis, and the imaginary numbers the y axis. The rest of the plane is given over to complex numbers.
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Umm... Hang on a tick. If one talks of imaginary numbers, these numbers would need to exist with an imaginary axis. Coupling an imaginary axis with a real axis would produce an Argand Plane (I think). For imaginary numbers to coexist with a real plane (two dimensions) one would need to have a 3-D space with two axes as real and one as imaginary. I guess then the answer is no unless one redefines the space into a Complex-Real Space. Or something.
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Real and imaginary numbers are one way of describing a 2D space. They don't so much coexist as describe that space: they are the co-ordinate, the fabric of the space. The real numbers, on their own, are a 1D space stretching from minus infinity through zero to plus infinity.
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Your question implies that real numbers exist in a 2-dimensional space. Normally they exist on a 1-dimensional number line, unless you're talking about an X-Y Cartesian plane, with two real axes. So I'm confused about what your question is. If you mean imaginary numbers on a Cartesian plane, the answer is NO because imaginary and complex numbers require an axis that is orthogonal (perpendicular) to the real axes. When dealing with complex numbers, even a simple function of one variable requires a total of 4 dimensions to graph the entire function. Often, various 3-D "slices" are visualized by us humans.
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