Polar coordinates and complex numbers

Remark — A look ahead: complex numbers

In the chapter on complex numbers the polar coordinate of $z = x+iy$ is precisely the pair $(\rho,\theta)$: $z = \rho(\cos\theta + i\sin\theta) = \rho\,e^{i\theta}$ (Euler’s form). Polar coordinates are therefore the natural language for multiplying complex numbers and raising them to powers.

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Topics: Goniometry
Concepts: Polar coordinates · Complex numbers · Cartesian plane