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Bear with me on this one please. I am learning about complex numbers.

We have cartesian coordinates made up of real numbers for points in cartesian plane.

Is there any plane in which we can have cartesian coordinates made up of complex number for points in that space? I am unable to visualize any such plane. Thanks in advance.

KawaiKx
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    You're asking about $\Bbb C^2$, which you can think of as $\Bbb R^4$ with some additional structure. – J.G. Aug 11 '22 at 14:51
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    We call it $\mathbb C^2.$ It is hard to visualize because it has four real dimensions. It can be called the "complex affine plane." There is a relatively nice number system that can be formed on it, the quaternions. – Thomas Andrews Aug 11 '22 at 14:52
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    This is a good question which (I think) has no good answer. It's hard to visualize that space, but you can do analytic geometry there, using complex numbers rather than real numbers. So you can study "lines" and imagine the graph of a complex function of a complex variable. – Ethan Bolker Aug 11 '22 at 15:10
  • For instance, the Riemann zeta function lives there. They look at slices or something to get pictures. – calc ll Aug 11 '22 at 16:08
  • And the Gamma function... – calc ll Aug 11 '22 at 16:12

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