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Complex analysis: * EQN:e^{i\theta}=\cos(\theta)+i.\sin(\theta) where /e/ is Euler's Number: 2.71828... In the special case EQN:\theta=\pi this reduces to Euler's Identity. The functions /cos/ and /sin/ come originally from trigonometry, and it's just a little bit magical that they turn up in a purely algebraic context. Interestingly, the formula also means that in some cases you can take logarithms of negative numbers. Specifically: | EQN:\log(z)=\log(r.e^{i\theta})=\log(r)+i.\theta | The log is not unique, though, because the same number /z/ is represented by infinitely many values of EQN:\theta.