Last time I opened with basic exponentiation and raised it to the idea of complex exponents (which may, or may not, have been surprising to you). I also began exploring the ubiquitous exp function, which enables the complex math needed to deal with such exponents.

The exp(x) function, which is the same as e^x, appears widely throughout physics. The complex version, exp(ix), is especially common in wave-based physics (such as optics, sound, and quantum mechanics). It’s instrumental in the Fourier transform.

Which in turn is as instrumental to mathematicians and physicists as a hammer is to carpenters and pianos.

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