Last time I introduced complex numbers, and how to think about multiplying them: they scale and rotate.
This time we studied pure rotations (i.e. scaling by 1), and showed that if there's any justice, the complex number z such that multiplying by z implements rotation by theta, should be z = exp(i theta).
This gave us formulae for sin and cos in terms of complex exponentials, which is good because the latter are much easier to work with.
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