Editing Phasor (section)

==Notation==
{{see also|Vector notation}}

'''Phasor notation''' (also known as '''angle notation''') is a [[mathematical notation]] used in [[electronics engineering]] and [[electrical engineering]]. A vector whose [[polar coordinates#Complex numbers|polar coordinates]] are magnitude <math>A</math> and [[angle]] <math>\theta</math> is written <math>A \angle \theta.</math><ref>{{cite book |last1=Nilsson |first1=James William |url=https://books.google.com/books?id=sxmM8RFL99wC |title=Electric circuits |last2=Riedel |first2=Susan A. |publisher=Prentice Hall |year=2008 |isbn=978-0-13-198925-2 |edition=8th |page=338}}, [https://books.google.com/books?id=sxmM8RFL99wC&pg=PA338 Chapter 9, page 338]</ref> <math>1 \angle \theta</math> can represent either the [[Euclidean vector|vector]] <math>(\cos \theta,\, \sin \theta)</math> or the [[complex number]] <math>\cos \theta + i \sin \theta = e^{i\theta}</math>, according to [[Euler's formula]] with <math>i^2 = -1</math>, both of which have [[magnitude (mathematics)|magnitudes]] of 1.

The angle may be stated in [[degree (angle)|degrees]] with an implied conversion from degrees to [[radian]]s. For example <math>1 \angle 90</math> would be assumed to be <math>1 \angle 90^\circ,</math> which is the vector <math>(0,\, 1)</math> or the number <math>e^{i\pi/2} = i.</math>

Multiplication and division of complex numbers become straight forward through the phasor notation. Given the vectors <math>v_1 = A_1 \angle  \theta_1</math> and <math> v_2 = A_2 \angle  \theta_2 </math>, the following is true:<ref>{{cite book |last1=Rawlins |first1=John C. |title=Basic AC Circuits |date=2000 |publisher=Newnes |isbn=9780750671736 |pages=427-452 |edition=Second |url=https://www.sciencedirect.com/science/article/pii/B9780750671736500146}}</ref>

:<math> v_1 \cdot v_2 = A_1 \cdot A_2 \angle (\theta_1 + \theta_2) </math>,

:<math>\frac{v_1}{v_2} = \frac{A_1}{A_2} \angle (\theta_1 - \theta_2)</math>.