Is it appropriate to include actual maths in a mathematics personal statement?
Here's the thing about personal statements in math: a bad one can hurt you, but a good one doesn't help you all that much. Your grades and letters are what will get the committee's attention and convince them that you're smart. You don't have to use the personal statement to keep convincing them that you're smart. The goal is more to demonstrate that you know what grad school in math is generally all about. It's also good if your enthusiasm shines through, but don't try too hard. For example, talking about how much you loved math as a kid would just be trite.

To answer the question: yes, it's probably fine to include a formula that you really like, and talk a bit about how it captured your imagination. But it's better if you can relate this to your future plans, because that is what the statement should be focused on. 

And again, don't formula-drop to look smart, especially not if the formula is something everyone learns in a first course in complex analysis (because knowing it doesn't set you apart from other applicants).

The above advice assumes you're applying for a graduate program. If you're applying for a summer REU or something similar, the same advice mostly applies, but there is less of an expectation that you know what your future plans are. But you can still tie your enthusiasm for Cool Identity X to your desire to learn more advanced math and get a taste of research through whatever program you're applying to.