In school I have been annoyed that we haven't been taught much of the intuition behind complex numbers so I made this little program. I am not satisfied with it yet but here it is anyways.
This is a very simple program that shows three complex numbers in the complex plane. An operation on the orange and the blue number is chosen by the user. The blue number is the output of that operation. The orange and the green numbers can be moved around and it can be observed how the blue number changes. In the image it can be seen that the orange number times it's conjugate (the green number) equals the magnitude of the green and the orange number squared (the blue number).
To use this program you must download this project and the love2d application from https://love2d.org/. Then drag the downloaded folder onto the love2d-app. Now you are ready to learn about complex numbers!
Holding shift will move the cursor in 0.25 increments. Drag the numbers around with the cursor. To change operation press tab or click the rectangle where the operation symbol is displayed.