# conjugate

1. ### Quuadratics whose real, irrational roots are NOT conjugate pairs

Quadratics whose real, irrational roots are NOT conjugate pairs Please bear with me as I'm not sure how to articulate this question succinctly. Often, when quadratic equations have real, irrational roots, they occur in conjugate pairs, but not always. (Contrast this with imaginary roots that...
2. ### If a^2 conjugate to a then a^{2^k} conjugate to a.

Let G be a group and p a prime such that a^p = 1 for all a in G. If p is odd and a is in G and a^2 = xax^{-1} for some x, then a^{2^k} = x^kax{-k} for k >= 1. I tried to prove this but all my efforts were in vain. Any idea how this can be proved?
3. ### Finding the limit by the conjugate

I'm stuck as to what to do next. The numerator can be factorized and if I plug in 0 for h, then the denominator will be zero which means it's undefined. Did I do anything wrong here?
4. ### Complex conjugate questions

Hey guys and girls. I have problem with these questions and im sorry if the questions sounds wierd, but im trying to translate from swedish to english. 1- indicate the Complex conjugate for −4−2i 2- Please indicate on the form a + bi is a complex number z has absolute value of 5 and the...
5. ### Limit of a complex function with cubed conjugate

Hello everyone, I'm working a problem set on complex analysis and encountered this limit, which I'm not sure how to solve. This is what I did. Can anybody tell me wether it is correct or how to compute it properly? Thank you very much!
6. ### Proof using magnitude & conjugate properties (Complex Analysis)

(Hint: No need to change to x and y form) If , use the properties of magnitude, conjugate, etc. to prove: I'm just confused on where to start. I have all my notes on the properties on of magnitude and conjugate but I don't know how to apply them. Any hints on how to tackle this bad boy?
7. ### Conjugate subgroups

Let G be a group and let g be some element of G. Given that \tau is an isomorphism is such that \tau(g) = g_1, show that S(g) and S(g_1) are conjugate subgroups of G. Here, S(x) is the subgroup of the set of automorphisms of G that fix the element x. In other words, S(x) = \{\sigma\in Aut G...
8. ### matrix groups and conjugate subgroups?

Question about matrix groups and conjugate subgroups?This question concerns the group of matrices L = { (a 0) (c d) : a,c,d ∈ R, ad =/ 0} under matrix multiplication, and its subgroups H = { (p 0, (p - q) q) : p,q ∈ R, pq =/ 0} and K = { (1 0, r 1) : r ∈ R} Show that one of H and K is a normal...
9. ### Adjoint vs complex conjugate

As I understand it, the adjoint of a matrix is also the complex transpose...but what's the difference between that and the complex conjugate of a matrix. How/why are the two used differently...?
10. ### Finding the # of elements of a group that are not in any conjugate to its subgroup

Also, just to be clear does G\H denote the right cosets where H<G and Hg = (hg: such that h is an element of H)?
11. ### Size of conjugate classes . (Abstract Algebra class)

What is the size of the conjugate classes of (12)(34) in Sn? I tried to solve it. I was able to deduce that " the conjugate classes of (12)(34) are those with the same structure so I assumed that I will have the following general conjugate class (ab)(cd), no matter how big n is. But I was not...
12. ### Matrix groups and conjugate

Please see attached file. I understand that for part a K is a normal subgroup of L through strategies eventually equating with a lower traingular matrix such like L. But when i try to manipulate H i end up with a really weird final result?! such as fractions and a lengthy multiplication in the...
13. ### Conjugate of a convex function

Hey guys, Does anyone have a clue how to calculate the conjugate of a log-sum-exp function?? log(summation(i=1...n) exp(xi))?? the conjugate of a function is defined as sup(Yx-f(x)) where Y is transposed. Thanks in Advance!!
14. ### for this limit problem do I multiply by the conjugate?

when I multiply by x+sqrt(x^2+2x) I get a denominator of zero. Does that mean I should divide thru by x to get 1+sqrt(1+2) That does not seem right either.
15. ### Complex numbers: Equation containing power and conjugate

I am asked to solve z^3 + conjugate(z) = 0 I have already attempted to solve it by replacing z with x + yi but I wasn't successful, what is the correct way to go about solving this ?
16. ### Conjugate of an Integral

A problem with integrals in the form of an example: "A trigonometric polynomial is a function f:R->C of the form f(x) = Sum{n=1,k} a_n exp(im_n k), x in R, k in N, the a_i in C, m_i in R. Show that <f,g> = lim(T->infinity) (1/2T) Int{-T,T} f(x)g*(x) dx defines an inner product on the linear...
17. ### How do you find the conjugate of -2/i^3?

What is the conjugate of \frac{\ -2}{i^3}?
18. ### Bayesian inference about conjugate prior integration

Hello, I am wanna understand how to integrate out some conjugate prior, particularly in high dimension form. its principal is simple, just find the right piece of terms for one specific distribution and integrate out. the challenging part is in high dimension and in matrix form. Please see...
19. ### Complex Conjugate Roots and the Quadratic Formula

Hello, there. I have the quadratic equation x^2+2x+7=0 Using \begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \\ \end{array}, I get \begin{array}{*{20}c} {x = \frac{{ - 2 \pm \sqrt {-24} }}{{2}}} \\ \end{array}. Now, I know the answer to this question is two...
20. ### simple conjugate question

Hi all, what is the conjugate of A + A exp(-i)+ B exp(-2i) regards,