• jsomae@lemmy.ml
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    24 hours ago

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

    ex+𝘪θ := ex(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.

    • shapis@lemmy.ml
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      21 hours ago

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

      • jsomae@lemmy.ml
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        16 hours 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.