Why is $1/i$ equal to $-i$? - Mathematics Stack Exchange
May 11, 2015 · 11 There are multiple ways of writing out a given complex number, or a number in general. Usually we reduce things to the "simplest" terms for display -- saying $0$ is a lot …
calculus - Evaluating $\int \frac {1} { {x^4+1}} dx$ - Mathematics ...
The integrand $\frac {1} {1+x^4}$ is a rational function (quotient of two polynomials), so I could solve the integral if I can find the partial fraction of $\frac {1} {1+x^4}$.
Evaluating $\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$
Sep 13, 2016 · Compute: $$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product. Is the product till infinity equal to $1$? If no, what is the answer?
What does $QAQ^ {-1}$ actually mean? - Mathematics Stack …
Apr 28, 2020 · I'm self-learning Linear Algebra and have been trying to take a geometric approach to understand what matrices mean visually. I've noticed this matrix product pop up repeatedly …
Intuition for volume of a simplex being $\frac 1 {n!}$
Jul 19, 2022 · The volume of this simplex is $\frac {1} {n!}$, but I am intuitively struggling to see why. I have seen proofs for this and am convinced, but I can't help but think there must be a …
What is the value of $1^i$? - Mathematics Stack Exchange
Aug 30, 2010 · There are infinitely many possible values for $1^i$, corresponding to different branches of the complex logarithm. The confusing point here is that the formula $1^x = 1$ is …
Banach Matchbox Problem - Mathematics Stack Exchange
Nov 8, 2014 · Banach Matchbox Problem: Suppose a mathematician carries two matchboxes at all times: one in his left pocket and one in his right. Each time he needs a match, he is equally …
False Proof of 1=-1 - Mathematics Stack Exchange
Aug 24, 2016 · 1 Indeed what you are proving is that in the complex numbers you don't have (in general) $$\sqrt {xy}=\sqrt {x}\sqrt {y}$$ Because you find a counterexample.
Why is the determinant of a symplectic matrix 1?
Why is the determinant of a symplectic matrix 1? Ask Question Asked 13 years ago Modified 1 year, 10 months ago Viewed 15k times
Why the Laplace transform of the integral is 1/s?
My only suggestion would be that you should adjust your terminology a bit. The Laplace transform of the integral isn't $\frac {1} {s}$. It'd be more accurate to say The Laplace transform of an …