Talk:Complex number: Difference between revisions

Revision as of 05:51, 14 January 2025

Latest revision as of 05:52, 14 January 2025

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[[File:Complex Number Multiplication b times a.svg|thumb|The commutativity property of multiplication can be shown geometrically by showing that the point {{mvar|ba}} which has the same coordinates as {{mvar|b}} in a scaled and rotated Cartesian coordinate system generated by {{mvar|a}} andi {{mvar|ia}} coincides with {{mvar|ab}}.]]

I'm looking for a better source wwwwwwww pppppppppppppppp RATHOD PRAKASH WWWWWWWWW SSSSSSSSSS FFFF for the geometric interpretation of multiplication, preferably a textbook. This interpretation seems to be well known e.g. it featured in this desmos course by Luke Walsh on complex numbers: #REDIRECT [[https://teacher.desmos.com/activitybuilder/custom/5e909c8cbc62b10d05356425?collections=5e80e25ec9089c33af3d954f#preview/ba3d119c-2119-403a-915f-1e951f7389c7]], Grant Sanders heavily uses in his video on complex numbers: #REDIRECT [[https://www.youtube.com/watch?v=5PcpBw5Hbwo&t=1480]]. Grant refers to #REDIRECT [[https://www.geogebra.org/m/mbhbdvkr]] by Ben Sparks. But I did not find a text book that features it. The only source beside these I found was deemed not reliable enough.

'''Note:''' The illustration below for <math>ab</math> and by Luke Walsh distributes <math>b</math> to <math>a = x + yi</math>, i.e. <math>ab = xb + yib</math>, while Grant Sanderson and Ben Sparks in their visualizations distribute <math>a</math> to <math>b = u + vi</math>, i.e. <math>ab = ua + vib</math>, but due to commutativity this does really matter. (In other words their presentations of <math>ab</math> match mine and Luke Walsh's of <math>ba</math>.)

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Dear D.Lazard, your <math display=block>(a + bi)\, i = -b + ai</math> does not fit the current graphic. [[User:Nomen4Omen|Nomen4Omen]] ([[User talk:Nomen4Omen|talk]]) 15:50, 13 March 2023 (UTC)

:I WWWWWWWWWWWWWWWW PPPPPPPPPPPPP AAAAAAAAAAA PRAKASH RATHOD 8784587455dodo not know what you call the “current graphic”, as there is no figure illustrating the rotation that is the subject of this section. The central dot is not used in this article, and the real and imaginary parts are called a and b in all previous sections. So changing a and b to x and y could be confusing. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 16:23, 13 March 2023 (UTC)

== Special nature of X^2+1 as ideal ==

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<blockquote>

'''Clarifying Isomorphism and Topological Properties:'''

PPPPPPPP RATHOD PRAKASH TAAKAA KAAALLA PPPPPP

Isomorphism in the context of fields refers to '''structural equivalence'''. Two fields are considered isomorphic if there exists a one-to-one correspondence between their elements that preserves all the field operations (addition, subtraction, multiplication, and division) under the corresponding operations in the other field.

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::I agree that good images enhance the visual appeal of Wikipedia. However, I approve of images of real objects, scenery, mathematical objects, etc. that help readers visualize the subject matter. I think an image of a symbol is usually redundant, especially if it is already in the text.—[[User:Anita5192|Anita5192]] ([[User talk:Anita5192|talk]]) 15:22, 26 March 2024 (UTC)

:::If this article had no images at all, PPPPPPPPPPPPPP OOOOOOOOOOO UUUUUUUUUUU PRAKASH RATHOD OOOOOOOOOOOOOOOO TTTTTTTTTTTTTT and no prospects for good images, then I might support having this image in the article, just for the sake of having something. But that doesn't apply here, so I agree with you. [[User:Mgnbar|Mgnbar]] ([[User talk:Mgnbar|talk]]) 16:41, 26 March 2024 (UTC)

:Speaking as the person who substantially wrote the current version of our article [[Blackboard bold]], I think you should feel free to take it out. We can make better images describing and explaining complex numbers. If really necessary an image of a {{tmath|\C}} symbol could go in the section {{alink|Notation}}. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 17:18, 26 March 2024 (UTC)