View source

'''Cis''' notation is a [[polar form | polar]] notation for [[complex number]]s. For all complex numbers <math>z</math>, we can write <math>z=r\mathrm{cis }(\theta)=r\cos \theta + ir\sin \theta</math>. Notice that <math>\mathrm{cis}</math> is made up by the first letter of <math>\cos</math>, <math>i</math>, and the first letter of <math>\sin</math>.

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

<math>e^{i\theta} = \cos \theta + i \sin \theta.</math>

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 

<math>\mathrm{cis}(r\theta) = (\mathrm{cis}(\theta))^r.</math>

This is more easily understood in the complex exponential form:

<math>e^{i(r\theta)} = (e^{i\theta})^r.</math>

== See also ==

* [[Complex numbers]]
* [[Polar form]]

[[Category:Complex numbers]]