The discussion clarifies that imaginary numbers can be represented on a two-dimensional x/y axis graph, specifically within the complex plane, where the horizontal axis denotes the real component and the vertical axis denotes the imaginary component. However, numbers that require a three-dimensional representation, such as quaternions, exist. Quaternions consist of one real component and three imaginary components, exemplified by the expression w = 2 + 1i - 2j + 3k.
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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:If I understand correctly an imaginary number can be graphically shown in a x/y axis graph.
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.thetexan said:Are there numbers that can only be graphed by using the third z axis? What are they called?