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Listen here, Little Dicky (mander.xyz)
submitted 4 days ago by [email protected] to c/[email protected]
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[-] [email protected] 12 points 3 days ago

This very nice Romanian lady that taught me complex plane calculus made sure to emphasize that e^j*theta was just a notation.

Then proceeded to just use it as if it was actually eulers number to the j arg. And I still don’t understand why and under what cases I can’t just assume it’s the actual thing.

[-] [email protected] 3 points 2 days ago* (last edited 2 days ago)

e^𝘪θ^ is not just notation. You can graph the entire function e^x+𝘪θ^ across the whole complex domain and find that it matches up smoothly with both the version restricted to the real axis (e^x^) and the imaginary axis (e^𝘪θ^). The complete version is:

e^x+𝘪θ^ := e^x^(cos(θ) + 𝘪sin(θ))

Various proofs of this can be found on wikipeda. Since these proofs just use basic calculus, this means we didn't need to invent any new notation along the way.

[-] [email protected] 2 points 2 days ago

I'm aware of that identity. There's a good chance I misunderstood what she said about it being just a notation.

[-] [email protected] 2 points 2 days ago

It's not simply notation, since you can prove the identity from base principles. An alien species would be able to discover this independently.

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this post was submitted on 01 Jul 2025
459 points (98.7% liked)

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