Prove that $e^ {i\pi} = -1$ - Mathematics Stack Exchange
Oct 13, 2021 · Prove Euler's identity $e^ {i\theta} = \cos \theta + i \sin \theta$ using Taylor series. Then plug in $\theta = \pi$.
How does $e^ {\pi i}$ equal $-1$ - Mathematics Stack Exchange
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.
Why does $e^{i\\pi}=-1$? - Mathematics Stack Exchange
Euler's formula describes two equivalent ways to move in a circle. Starting at the number $1$, see multiplication as a transformation that changes the number $1 \cdot e^ {i\pi}$. Regular exponential …
Am I wrong in thinking that $e^ {i \pi} = -1$ is hardly remarkable?
I believe my trouble is that the identity, $e^{i \\pi} = -1$, comes down to the definition of the exponentiation of $i$, which seems rather obscure to me. This is my ...
Explain why $e^ {i\pi} = -1$ to an $8^ {th}$ grader?
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 …
Why is $ (-1)^x=e^ {i\pi x}$ - Mathematics Stack Exchange
Aug 6, 2015 · I was recently taught exponentials and I decided to play around with negative bases, which they told me were not allowed. The obvious place to start was negative one, and, as expected, …
Why $e^{i(π/3)} \\ne -1$? - Mathematics Stack Exchange
Mar 30, 2018 · Want to improve this question? As written, this question is lacking some of the information it needs to be answered. If the author adds details in comments, consider editing them …
complex numbers - Is $i = \sqrt {e^ {\pi\sqrt {e^ {\pi\sqrt\ldots ...
Feb 8, 2015 · e^ipi = -1. If you do the square root of that you get i = sqrt (e^ipi), but i has just been defined to sqrt (e^ipi), and so it goes on.
$e^ {\pi i} = -1$ is this a fact or an assumption?
Mar 8, 2021 · I think it is a fact but can someone explain why is it true intuitively? I heard a lot of videos on youtube assuming it is the "natural" way of revolving around 0, many other …
How can $i^i = e^ {-\pi/2}$ - Mathematics Stack Exchange
Apr 19, 2017 · Then go build some other numbers which behave the way you want instead.