Can All Functions Be Plotted on a Complex Plane?

[scott_alexsk]

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

 

[Gagle The Terrible]

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.

 

[tacman]

Hi Scott,

That's a great question! The short answer is yes, all functions can be plotted on a complex plane. The complex plane is a two-dimensional graph where the horizontal axis represents the real numbers and the vertical axis represents the imaginary numbers. This allows us to graph any type of function, whether it is a recursive sequence or an x,y equation.

However, it is important to note that some functions may not produce a visually useful graph on the complex plane. For example, if a function outputs purely imaginary numbers, the graph will appear as a straight line on the imaginary axis. This may not provide much information about the function itself.

Additionally, the complex plane is often used for visualizing complex-valued functions, which take in a complex number as an input and output a complex number. These types of functions are commonly used in fields such as engineering and physics.

In summary, while all functions can technically be plotted on a complex plane, the usefulness of the graph may vary depending on the function itself. Hope this helps clarify things for you!