Complex Numbers Explorer

Inspiration

We all know how we can graph a Mathematical Equation. For linear equations it's a straight line, for quadratic equations it's a parabola and so on. These equations usually have a real number variable x in them. I wondered how if the variable be z, a complex number. It was the Idea behind Graphing Complex numbers. And after researching upon the internet for solutions I stumbled upon a website Complex Function Grapher made by Dan Jutan, which used a solution for graphing complex functions called Complex Domain Coloring. So, then I made a enhanced and simplified version of that and made this project Complex Number Solver and Grapher.

Complex Domain Coloring

Domain coloring makes every input complex number a point on a 2D graph, and every output complex number a color. It then colors each input point with its corresponding output color. The color for a complex number is calculated from it's magnitude and angle.

What it does

Complex Number Solver and Grapher is a handy tool for you if you are working with complex numbers. It can solve Mathematical equations containg a complex number and give you the answer. Additionally it also calculates some extra information about the complex number answer such as Modulus, Argument and Polar Form of the answer.

You can also Graph a Mathematical Equation containing a complex number variable z. It will let you see how beautiful patterns could emerge from Complex Numbers.

How we built it

I built this app so that everyone can use it easily. So I made this app on a platform called MecSimCalc which provides a nice GUI for users. Python was used as the programming language for all coding and mathematical logic. I used python's inbuilt cmath library for computations on complex numbers.

Challenges we ran into

It was difficult to plot a complex function. Firstly, I checked some python libraries for help but found that no library can do what I wanted to ( or maybe I didn't understand how to use those libraries for advanced use ). Then I decided to manually draw individual pixels on an image to show the graph for which I used the Pillow python library.

Accomplishments that we're proud of

I made an app which can become a handy tool for students learning about complex numbers, engineers and scientists. It shows the beauty of Complex Numbers.

What we learned

Before this I thought that Complex Functions cannot be graphed on a 2D surface. Now I learned how to graph them. I learned many usecases of Complex numbers in daily life. I understood how they work.