Jan
19
comment Complex numbers modulus/argument question
It can be transformed to $$\frac{\text{Im}(z)}{1-\text{Re}(z)}i$$.
Jan
18
comment Complex numbers modulus/argument question
Yes, I now I see this. But then it is possible to simplify $|1-z|^2$ further.
Jan
18
comment Complex numbers modulus/argument question
why does the $|1-z|^2$ disappear
Jan
18
comment Calculation of the derivative of $e^{\cos(x)}$ from first principles
calculating the derivate uses the chain rule and the rules for $\cos$ and $\exp$. So you could try to mimic a proof of the chain rule.
Jan
18
comment Find the maximum value
The derivate is $$\left(1-2\,y\right)\,\left(y-y^2\right)\,\int_{0}^{y}{{{1}\over{ \sqrt{\left(y-y^2\right)^2+x^4}}}\;dx}+\sqrt{\left(y-y^2\right)^2+y^ 4}$$. I is $>0$ if $y \in (0,\frac{1}{2})$ becaus every factor is $>0$. So The integral is increasing in this interval. One can underestimate the integral and show that it is positive in the remaining interval. But there are much simpler solutions.
Jan
18
comment Find the maximum value
+1 much more simpler than using Leibniz's rule
Jan
18
comment Find the maximum value
I think you can use Leibniz's integration rule: if $$g(y)=\int^{b(y)}_{a(y)} f(x,y) dx$$ then $$g'(y)=\int_{a(y)}^{b(y)}\frac{df}{dy}(x,y)+f(b,y)b'(y)-f(a,y)a'(y)$$ to investigate the integral
Jan
11
comment How would I solve the following trig equation?
+1 I like your answers based on groebner basis
Jan
10
comment How find this function equation $(f(x))^2-(f(y))^2=f(x+y)\cdot f(x-y)$
@Ewan Delanoy: why do you think so?
Jan
8
comment Probability Exercise (Java and C++)
you are perfectly right
Jan
6
comment Factorize Polynomials
$(z^4 + z^3 + z) \equiv (z^2 + 1) *(z^2 + z +1)+1\pmod{2}$, so $h \equiv 1 \pmod{2}$
Jan
4
comment Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
+1 but I think $f_2(x) = (x^2+x+1)(x^3+x^2+1)$
Jan
4
comment Procedure for showing a polynomial is irreducible in $\mathbb{Q[x]}$
@user115654: thank you. I worked whith a cas (maxima). When I printed out the TeX string for the polynomials to paste them into this post I had already assigned values 12 and 1 to the symbols "d" and "e" (the last line in the table!). I corrected this error.
Dec
29
comment Linear Dependence Of A Sum
@Henning Makholm: Thanks, done
Dec
27
comment Linear Dependence Of A Sum
i noticed that i have downvoted this by accident about an hour ago. It is not possible to undo this downvote now. sorry.
Dec
19
comment Simplifying an equation
I think the correct notation is $$\frac{du}{dt}=2t$$ and so on which is generated by $$\frac{du}{dt}=2t$$.
Dec
12
comment Counterexample to Eisenstein criterion
@Git Gud: This question makes sense. if one removes condition "$p$ is prime" by "$p$ is an arbitrary integer" then the statement is wrong.
Dec
5
comment Is $x^4+x+1$ irreducible in $\Bbb{Q}[x]$?
$f(5)=631$ is a prime so f(x) is irreducible. See math.stackexchange.com/questions/568094/…
Dec
5
comment Is $x^4+x+1$ irreducible in $\Bbb{Q}[x]$?
you should do this $\pmod 2$. Otherwise you have to investigate $(x^2+ax \pm 1)(x^2+bx \pm 1)$
Dec
5
comment How to find the minimum of $a+b+\sqrt{a^2+b^2}$
I think the angle at $0$ is $90^\circ$ and $Q$ is the intersection of that angle bisection in $0$ and a normal to $AB$ in $P$. But $|OE|+|OF|+|EF|=|OA|+|OB|+AB|$ is still unclear to me.