Difference between revisions of "Polar form"
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The polar form for [[complex number]]s allows us to graph complex numbers given an [[angle]] <math>\theta</math> and a [[radius]] or [[magnitude]] <math>r</math>. | The polar form for [[complex number]]s allows us to graph complex numbers given an [[angle]] <math>\theta</math> and a [[radius]] or [[magnitude]] <math>r</math>. | ||
| − | For <math>z\in\mathbb{C}</math>, we can write <math>z=r\mathrm{cis }(\theta)=r(\cos \theta+i\sin\theta)</math>. (See [[cis]] if you do not understand this notation.) This represents a complex number <math>z</math> that is <math>r</math> units away from the origin, and <math>\theta</math> [[radian]]s counterclockwise from the positive half of the <math>x</math>-axis. | + | For <math>z\in\mathbb{C}</math>, we can write <math>z=r\cdot\mathrm{cis }(\theta)=r(\cos \theta+i\sin\theta)</math>. (See [[cis]] if you do not understand this notation.) This represents a complex number <math>z</math> that is <math>r</math> units away from the origin, and <math>\theta</math> [[radian]]s counterclockwise from the positive half of the <math>x</math>-axis. |
== See also == | == See also == | ||
Latest revision as of 12:35, 1 April 2022
Polar form for complex numbers
The polar form for complex numbers allows us to graph complex numbers given an angle 
and a radius or magnitude 
.
For 
, we can write 
. (See cis if you do not understand this notation.) This represents a complex number 
that is units away from the origin, and radians counterclockwise from the positive half of the 
-axis.
