Can All Functions Be Plotted on a Complex Plane?

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All functions can be plotted on a complex plane, but the representation differs from the standard xy-plane due to the definition of the dot product. While recursive sequences like the Mandelbrot Set are commonly visualized, it's also possible to plot x,y equations by ignoring the real part of the y output. The complex plane allows for unique visualizations, particularly with fractals, which utilize the imaginary part of numbers in ways that the xy-plane cannot. The capabilities of plotting functions depend on the software used. Overall, the complex plane offers a broader range of graphical representations for various mathematical functions.
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complex plane

Hello, I was wondering if there are only specific types of forumlas that you can graph on a complex plane. I mean can you only plot recursive sequences such as the Mandelbrot Set or can you also plot x,y equations while just ignoring the real part of the y output.
Thanks,
-scott
 
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Well, to start off, the "only" difference between the complex plane and the standard xy-plane is how the dot product is defined. Now how the plot functions can be used depending of the software is a vague question.
Fractals, as you mentionned, use the imaginary part of the number(and its properties) in a way that no xy-plane can, even if it can plot recursive functions.
 

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