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It's the exponential notation for complex numbers, see for example https://tutorial.math.lamar.edu/Extras/ComplexPrimer/Forms.aspx https://tutorial.math.lamar.e

• sillysaurusx 5y ago
  That post proves the point: it jumps from "use cos(t) + i sin(t)" to "use e^it" with zero explanation about why it's related to 2.718281828... The reason I posted my comment is because e^(i pi) is obviously supposed to be -1+0j. But I see now that I was using the calculator incorrectly (I was doing the equivalent of πe^i) but there was a bug in the parenthesis operator preventing me from typing it that way on mobile.
  • Tubeee 5y ago
    > it jumps from "use cos(t) + i sin(t)" to "use e^it" with zero explanation about why it's related to 2.718281828... It really isn't, beyond the fact that exp(1) = 2.718…. Then, by definition exp(it) = exp(1)^(it) = e^it. It isn't much more than a notational artifact as far as I'm concerned. For that matter, raising any base b to a power is equivalently just scaling it by ln(b) and plugging it into exponential function, that is, b^it = cos(ln(b) * t) + i sin(ln(b) * t).
    • sillysaurusx 5y ago
      That last equation clarified things greatly for me. Thanks.