Editing Imaginary number (section)

==Geometric interpretation==
[[File:Rotations on the complex plane.svg|thumb|90-degree rotations in the [[complex plane]]]]

Geometrically, imaginary numbers are found on the vertical axis of the [[Complex plane|complex number plane]], which allows them to be presented [[perpendicular]] to the real axis. One way of viewing imaginary numbers is to consider a standard [[number line]] positively increasing in magnitude to the right and negatively increasing in magnitude to the left. At 0 on the {{mvar|x}}-axis, a {{mvar|y}}-axis can be drawn with "positive" direction going up; "positive" imaginary numbers then increase in magnitude upwards, and "negative" imaginary numbers increase in magnitude downwards. This vertical axis is often called the "imaginary axis"<ref name=Meier>{{cite book|url=https://books.google.com/books?id=bWAi22IB3lkC|title=Electric Power Systems – A Conceptual Introduction|last=von Meier|first=Alexandra|publisher=[[John Wiley & Sons]]|date=2006|access-date=2022-01-13|pages=61–62|isbn=0-471-17859-4}}</ref> and is denoted <math>i \mathbb{R},</math> <math>\mathbb{I},</math> or {{math|ℑ}}.<ref>{{cite book|chapter=5. Meaningless marks on paper|title=Clash of Symbols – A Ride Through the Riches of Glyphs|last1=Webb|first1=Stephen|publisher=[[Springer Science+Business Media]]|date=2018|pages=204–205|doi=10.1007/978-3-319-71350-2_5|isbn=978-3-319-71350-2}}</ref>

In this representation, multiplication by&nbsp;{{mvar|i}} corresponds to a counterclockwise [[rotation]] of 90 degrees about the origin, which is a quarter of a circle. Multiplication by&nbsp;{{math|−''i''}} corresponds to a clockwise rotation of 90 degrees about the origin. Similarly, multiplying by a purely imaginary number {{mvar|bi}}, with {{mvar|b}} a real number, both causes a counterclockwise rotation about the origin by 90 degrees and scales the answer by a factor of {{mvar|b}}.  When {{math|''b'' < 0}}, this can instead be described as a clockwise rotation by 90 degrees and a scaling by {{math|{{abs|''b''}}}}.<ref>{{cite book|url=https://books.google.com/books?id=_2sS4mC0p-EC&pg=PA10|title=Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace, and Virtual Reality|last=Kuipers|first=J. B.|publisher=[[Princeton University Press]]|date=1999|access-date=2022-01-13|pages=10–11|isbn=0-691-10298-8}}</ref>