Recent content by tonit

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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    yeah, I'll keep that in my mind :smile:
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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    alright so after simplifying I get 16sin^4\theta - 12sin^2\theta + 1 = 0 now it's pretty obvious to solve. thanks :D
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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    I guess the first one would be easier, and I got 16sin^5\theta - 20sin^3\theta + 5sin\theta = 1 I'm stuck again...:@
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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    I got sin^5θ - 10sin^3θ cos^2θ + 5sinθ cos^4θ = 1 and i5sin^4θcosθ - i10sin^2θcos^3θ + icos^5θ = 0 where θ = \frac{\pi}{10} = 18^{\circ} is this ok?
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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    e^{i\frac{2\pi }{5}} = sin(18) + icos18 right?
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    Find 5th roots of unity solving x^5 -1=0 and use the result for sin18 and cos18

    Homework Statement Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution x^5 = 1\\ x = \sqrt[5]{1} since we have 5 roots: x_k, k = 0,1,2,3,4 \\ \\ x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...
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    Efficient Methods for Finding Inverses in Zn

    Thank you HallsofIvy. It's all clear now :D
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    Efficient Methods for Finding Inverses in Zn

    ok. Thank you!...very helpful
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    Efficient Methods for Finding Inverses in Zn

    Homework Statement Let's say I want to find the inverse of \bar{4} in \mathbb{Z}_{13}. So I get 13 = 4\cdot 3 + 1 and so 1 = 13 - 4\cdot 3. But this doesn't show that 3 is inverse of 4. So I have to express 4 = 3\cdot 1 + 1 which yields that 1 = 4 - 1\cdot 3 = 4 - 3\cdot (13 - 3\cdot 4) =...
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    What are the cyclic subgroups in Z6 x Z3?

    Direct product of two groups G and H, is the group G\times H = \{ (g,h) | g \in G, h \in H \}. If * is the operation of G and H, (g,h)*(g_1,h_1) = (g*g_1,h*h_1). Similarly the inverse (g,h)^{-1} = (g^{-1},h^{-1}). Now can you find any element (g,h) \in \mathbb{Z}_6\times \mathbb{Z}_3 such that...
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    G is cyclic and |G| = p^n, p is prime <=> H,K Subgroups, H⊆K or K⊆H

    If H and K are subgroups of G, suppose H⊆K. So we have that |H| divides |K|, and they both divide |G|. If it would happen that |G| = p^ka^r where p, a are different primes, then G would have two subgroups M and N such that |M| divides p, |N| divides a, M ⊄ N and N ⊄ M, thus contradicting the...
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    Equivalence Relations on {0, 1, 2, 3}: Understanding Reflexivity and Properties

    Reflexive doesn't mean a = a. The equality is a relation of equivalence, but a relation of equivalence need not be "=".
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    G is cyclic and |G| = p^n, p is prime <=> H,K Subgroups, H⊆K or K⊆H

    Homework Statement Show that the following conditions are equivalent for a finite group G: 1.G is cyclic and |G| = p^n where p is prime and n\geq 0 2.If H and K are subgroups of G, either H⊆K or K⊆H. The Attempt at a Solution 1 => 2. Let H,K be subgroups of G = <g> where o(g)...
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    C/C++ Guide to C++ Programming For Beginners

    Well, you should try to work with classes. As there is no way the program does it automatically for you. You should learn some OOP, and it will make your life easier when you work with C++. That's how program's work. They call functions. For example, each time you post something on the forum...
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    Show that G is abelian, if and only if (gh)^-1 = g^(-1) h^(-1)

    yeah. Thanks for the help, I'm learning a lot at this forum really :D