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 …

When I first found out that eiπ = −1 e i π = 1, I was blown away. Does anyone here know one of (many I'm sure) proofs of this phenomenal equation? I can perform all of the algebra to get the …

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

@ColeJohnson, eiπ = −1 e i π = 1 is a consequence of how the objects e e, π π and raising a number to the power of a complex number are defined. There is no deep truth behind the …

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 / …

Apr 19, 2017 · I was asked a homework question: find ii i i. The solution provided was as follows: Let A = ii A = i i. log A = i log i log A = i log i. Now, log i = logeiπ/2 = iπ2 log i = log e i π / 2 = i …

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?

Mar 22, 2014 · 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: $$|e^ {-2i}|=1, i=\sqrt {-1}$$

Euler’s formula states that eix = cos(x) + i sin(x) e i x = cos (x) + i sin (x). I can see from the MacLaurin Expansion that this is indeed true; however, I don’t intuitively understand how …

The point on the unit circle at an anti-clockwise angle θ from the positive x-axis is (cosθ, sinθ). Since 2π corresponds to a complete rotation, half a rotation will correspond to switching sign …