HackerEuler's formula with introductory group theory
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Further reading 1
Caption notes
Read an exponential as a map between actions: adding inputs corresponds to multiplying outputs. Mapping imaginary displacements to rotations makes addition of angles agree with complex multiplication; base e fixes the angular scale.
Creator’s caption track ↗Original passages · 2
adding the inputs corresponds with multiplying the outputsFunctions between groups that preserve the arithmetic like this are really important throughout group theory, enough so that they've earned themselves a nice fancy name, homomorphisms.