Euler's formula describes two equivalent ways to move in a circle. Starting at the number 1 1, see multiplication as a transformation that changes the number 1 ⋅eiπ 1 ⋅ e i π. Regular exponential …

I love how the OP said, "I put it into the calculator and it works". Love this, my favorite example of how non-intuitive math can be.

Apr 20, 2015 · @Jamie: FWIW, I first saw this fact outside of class in about 7th grade, saw it "formally" for the first time in pre-calculus, got a first non-rigorous proof in Calculus II, and wasn't able to prove …

Oct 13, 2021 · Prove Euler's identity $e^ {i\theta} = \cos \theta + i \sin \theta$ using Taylor series. Then plug in $\theta = \pi$.

Mar 30, 2018 · I understand why eiπ = −1 e i π = 1 and as a result ei2π =(eiπ)2 = 1. e i 2 π = (e i π) 2 = 1. These results can be confirmed using Euler's formula But why does eiπ/3 ≠ −1 e i π / 3 ≠ 1 as we …

Apr 19, 2017 · Then go build some other numbers which behave the way you want instead.

Apr 13, 2018 · Does Eulers formula give $$e^{-ix}=\\cos(x) -i\\sin(x)$$ I know that $$e^{ix}=\\cos(x)+i\\sin(x)$$ But how does it work when we have a $-$ in front

Jun 25, 2016 · I have two favorite arguments that we should have $\exp (i\theta)=\cos \theta +i\sin \theta$ for real $\theta$. The first is closely related to Mathologer's video e to the pi i for dummies, …

Jul 24, 2013 · Complex conjugation is an automorphism of order 2, meaning $\,\overline {\overline z}=z\,\,,\,\,\forall\,z\in\Bbb C\,$ , so if the conjugate of $\,e^ {-iwt}\,$ is ...

Possible duplicates: How does e, or the exponential function, relate to rotation?, How to prove Euler's formula: $\exp (it)=\cos (t)+i\sin (t)$?