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Euler's formula
This is one of them crazy things in mathematics. Kind of thing make you want to change career and be a researcher.
If you input imaginary numbers (multiples of \sqrt{-1}) into the exponential function you get the cosine and the sine function: \[ \exp(ix) = \cos(x) + i\sin(x) \]
I mean I am sure you already had some doubts that sine and cosine were related, but the exponential function? Now that is mad!
Definitions
- $z\in \mathbb{C}$: A complex number
- $Re\{ z \}$: The real part of $z$.
- $Im\{ z \}$: The imaginary part of $z$.
- $\frac{d}{dx}$: Derivative with respect to $x$
What is this for?
Allows you to deal with derivatives simply in AC circuits.