How is Euler’s Formula/Identity practical?

Question

For those who don’t know, and correct me if I’m wrong, Euler’s Formula is e^(xi) = cos(x) + isin(x) and Euler’s Identity is where “x” is equal to pi, therefore e^(πi) = -1. It’s fascinating to me how something so complex can be equal to something so simple (talking about Euler’s Identity). But what I don’t get is how they’re practical. What are they used for, and why are they important?

In: 3

Answer 1

The short answer is that it acts as a bridge between differential equation and trigonometry. It lets you use the tools of the one on the other and vice versa. It’s similar to the way DeCartes’ graphs were a bridge between algebra and geometry.