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Complex Graphing Calculator 2: Derivatives!

**Julius Won**

**September 14 2023**

Complex Graphing Calculator 2: Derivatives!

A while ago I coded a cool graphing calculator that graphed functions using the complex plane as the input and a wierd 4th axis to make a complex output.

First of all, I refactored everything. This means that it now looks a little less shiny, but a lot more professional. Also it runs way faster, has acutal control over domain and range, and a pause button. Funky.

The other thing I did was much more cool, which was programming a little bit of differential calculus into this thing. Now you can do tangent...planes? Yes, planes. While on a normy graph, slope can be shown with just one number, on this baby slope has 2: the rate of change of the real axis of the function, and the rate of change of the imaginary axis of the function. A plane can be angled with 2 slopes, making it the perfect representation for slope.

One important note: if you code this yourself, you can either: analytically differentiate the function, or numerically do so. If the latter, you must make the limit aproach 0 from both the real and imaginary axis. So if h=a+bi, it must be the limit as both a and b aproach 0. Otherwise it gets wierd.