Online app which plots F(z) in the complex plane

In summary, the conversation discusses the need for an app that can quickly plot the function f(z) in the complex plane. The ideal app would allow the user to visualize f(z) while moving the mouse on the complex plane to the location of z. One possible application for this is to visualize the zeros of the Riemann zeta function by moving the mouse on the critical line. While the app "desmos" is suggested, it is unsure if it can handle complex values. Another app "academo.org" is mentioned, but it only plots in 3D and does not meet the requirements for a 2D plot of f(z).
  • #1
Adel Makram
635
15
I am looking for an app that can instantaneously plot the function f(z) in the complex plane once z is given.
It would be much favorable if this process is fast which allows one to visualize f(z) when the user is moving the mouse on the complex plane to the location of z.
One possible application, is to visualize the zeros of the Riemann zeta function if one move the mouse on the critical line.
 
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  • #3
jedishrfu said:
My goto one is desmos but I’m not sure if it will handle complex values.

I found this one though

https://academo.org/demos/3d-surface-plotter/
I took a look at this, but it doesn't seem to be what the OP needs. The graph of a complex function ##f : \mathbb C \to \mathbb C## requires four dimensions: two for the complex input and two more for the complex output. I don't have any good suggestions, though.
 
  • #4
Mark44 said:
I took a look at this, but it doesn't seem to be what the OP needs. The graph of a complex function ##f : \mathbb C \to \mathbb C## requires four dimensions: two for the complex input and two more for the complex output. I don't have any good suggestions, though.
I just need a 2D space, so that when I click any where in this plane (z), the app immediately plots the f(z) on the same plane. This should also draw f(z) as a continuous curve if the function is analytic.
 

1. What is F(z)?

F(z) is a mathematical function that takes a complex number z as its input and produces a corresponding complex number as its output. It is typically represented as F(z) = u(z) + iv(z), where u(z) and v(z) are real-valued functions of the complex variable z.

2. How does the online app plot F(z) in the complex plane?

The online app utilizes complex mapping techniques to plot F(z) in the complex plane. It maps the real and imaginary parts of the input complex number z onto the x and y axes, respectively, and then plots the resulting output complex number on the plane. This process is repeated for a range of input values to generate a visualization of the function in the complex plane.

3. What is the purpose of plotting F(z) in the complex plane?

Plotting F(z) in the complex plane allows for a visual representation of the behavior of the function. It can help in understanding the geometric properties and patterns of the function, as well as identifying important features such as zeros, poles, and singularities. This can be useful in various fields of mathematics and physics, including complex analysis, differential equations, and signal processing.

4. Can the online app plot any type of function in the complex plane?

Yes, the online app can plot any function that can be expressed in terms of complex numbers. This includes elementary functions such as polynomials, rational functions, exponential and logarithmic functions, as well as more complex functions like trigonometric and hyperbolic functions.

5. Is the online app accurate in plotting F(z) in the complex plane?

Yes, the online app uses precise mathematical algorithms to accurately plot F(z) in the complex plane. However, the accuracy of the plot may also depend on the precision of the input values and the complexity of the function itself. It is always recommended to verify the results with other sources or by hand calculations.

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