Polar form

Polar form for complex numbers

The polar form for complex numbers allows us to graph complex numbers given an angle $\theta$ and a radius or magnitude $r$.

For $z\in\mathbb{C}$, we can write $z=r\cdot\mathrm{cis }(\theta)=r(\cos \theta+i\sin\theta)$. (See cis if you do not understand this notation.) This represents a complex number $z$ that is $r$ units away from the origin, and $\theta$ radians counterclockwise from the positive half of the $x$-axis.

See also