✎ Imaginary Numbers [The Physics Travel Guide]

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====== Imaginary Numbers ======

<tabbox Why is it interesting?> 
Imaginary numbers are essential in modern theories of physics like [[theories:quantum_theory:quantum_mechanics|quantum mechanics]] and [[theories:quantum_theory:quantum_field_theory|quantum field theory]]. In these theories, we describe a physical system using complex functions, which means functions that contain combinations of imaginary numbers as arguments.

Moreover, imaginary numbers can often be used to make calculations simpler.

For some further motivation, see the nice list [[https://math.stackexchange.com/a/168/120960|here]].

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<blockquote>The shortest path between two truths in the real domain passes through the complex domain. <cite>J. Hadamard</cite></blockquote>

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**Important Related Concepts:**

* [[basic_tools:complex_analysis]]
<tabbox Layman>

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student>

* The best introduction is [[https://betterexplained.com/articles/a-visual-intuitive-guide-to-imaginary-numbers/|A Visual, Intuitive Guide to Imaginary Numbers]] by Kalid Azad
  * See also https://math.stackexchange.com/questions/199676/what-are-imaginary-numbers
 
<tabbox Researcher>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

--> Example1#

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</tabbox>

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