Trigonometric form and argument

Every point $(a;b)$ of the plane also has polar coordinates $(\rho,\theta)$, with $\rho=\sqrt{a^2+b^2}$ and $\theta$ the oriented angle with respect to the real axis. So every complex number can be written in trigonometric form: $z = \rho(\cos\theta + i\sin\theta).$

The angle $\theta$ is called the argument of $z$ ($\arg z$) and is defined up to multiples of $2\pi$: adding a full turn does not change the point represented. The modulus $\rho=|z|$ is the distance from the origin.

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Topics: Complex numbers
Concepts: Argument · Trigonometric form · Modulus
Skills: Use formulae