Can Numbers Only be Graphed Using the Z Axis and What are They Called?

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Imaginary numbers can be represented on a two-dimensional x/y graph, with the horizontal axis for real components and the vertical for imaginary components. However, there are numbers like quaternions that require a three-dimensional representation, utilizing an additional z axis for their imaginary components. Quaternions consist of one real part and three imaginary parts, exemplified by expressions such as w = 2 + 1i - 2j + 3k. No numbers exist that can only be graphed using the z axis alone without incorporating the x and y axes. Understanding these concepts is essential for visualizing complex mathematical structures.
thetexan
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If I understand correctly an imaginary number can be graphically shown in a x/y axis graph. Are there numbers that can only be graphed by using the third z axis? What are they called?

tex
 
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thetexan said:
If I understand correctly an imaginary number can be graphically shown in a x/y axis graph.
In the complex plane (also called the Argand plane), the horizontal axis is for the real component of a complex number, and the vertical axis is for the imaginary component. A purely imaginary number is represented by a point directly above or directly below the origin.
thetexan said:
Are there numbers that can only be graphed by using the third z axis? What are they called?
I don't believe so. There are numbers called quaternions that require four dimensions to graph -- one real dimension and three imaginary dimensions. An example of a quaternion is w = 2 + 1i - 2j + 3k, where i, j, and k are imaginary units.
 

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