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@jemoka / Jemoka Knowledge Base / wiki/concepts/euler_s_equation.md
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--- title: "Euler's Equation" type: concept source: https://www.jemoka.com/posts/kbheuler_s_equation/ confidence: high status: active --- \begin{equation} f(x) = e^{ix} = \cos (x) + i\sin (x) \end{equation} this brings a circle of radius one, because in every point, velocity is orthogonal to where you are (because \(f’(x) = if(x)\), and multiplying by \(i\) accounts for a rotation of 90 degrees. And so, \begin{equation} z = re^{i\theta} \end{equation} gives any point in the imaginary polar plane.