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 …

2021年10月13日 · Prove Euler's identity $e^ {i\theta} = \cos \theta + i \sin \theta$ using Taylor series. Then plug in $\theta = \pi$.

2015年4月20日 · @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 …

2010年8月28日 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and …

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.

Yes I am aware I was just stating how I got super curious about sinh but why do I get different answers for sinh (ipi) and (e^ (ipi) - e^ (-i*pi))/2?

2018年3月30日 · 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 …

2017年4月19日 · Then go build some other numbers which behave the way you want instead.

2015年2月8日 · Can somebody explain to me why the absolute value of a complex exponential is 1? (Or at least that's what my textbook says.) For example: $$|e^ {-2i}|=1, i=\sqrt {-1}$$

2021年10月25日 · How can I find all roots of logz=ipi/2? I tried to use the formula Logz=lnr+itheta, but I cannot do the next step.