Difference between revisions of "Cis"
Made in 2016 (talk | contribs) m (Made the link to De Movire's Theorem work.) |
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<math>e^{i\theta} = \cos \theta + i \sin \theta.</math> | <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 | + | This is so that one can more naturally use the properties of the complex [[Exponential form|exponential]]. One important example is [[De Moivre's Theorem]], which states that |
<math>\mathrm{cis}(r\theta) = (\mathrm{cis}(\theta))^r.</math> | <math>\mathrm{cis}(r\theta) = (\mathrm{cis}(\theta))^r.</math> | ||
Latest revision as of 19:59, 11 July 2023
Cis notation is a polar notation for complex numbers. For all complex numbers 
, we can write 
. Notice that 
is made up by the first letter of 
, 
, and the first letter of 
.
Once one gets used to the notation, it is almost always preferred to write 
rather than 
, 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:
