Cis

Cis notation is a polar notation for complex numbers. For all complex numbers $z$ , we can write $z=r\mathrm{cis }(\theta)=r\cos \theta + ir\sin \theta$ . Notice that $\mathrm{cis}$ is made up by the first letter of $\cos$ , $i$ , and the first letter of $\sin$ .

Once one gets used to the notation, it is almost always preferred to write $re^{i\theta}$ rather than $r\mathrm{cis }(\theta)$ , as Euler's formula states that

This is so that one can more naturally use the properties of the complex exponential. One important example is De Moivre's theorem, which states that

This is more easily understood in the complex exponential form:

See also