So the question is show that
$$S=\left\{ \begin{pmatrix} a & b\\ -b & a \end{pmatrix} :a,b \in \Bbb{R} ,\text{ not both zero}\right\}$$ is isomorphic to $\Bbb{C}^*$, which is a non-zero complex number considered as a group under multiplication
So I've shown that it is a group homomorphism by...
I'm trying to determine if \sum_{n=1}^{\infty}\frac{{n}^{10}}{{2}^{n}} converges or diverges.
I did the ratio test but I'm left with determining \lim_{{n}\to{\infty}}\frac{(n+1)^{10}}{2n^{10}}
Any suggestions??
Consider the subset of $S_4$ defined by
$$K_4=\{(1)(2)(3)(4),(12)(34),(13)(24),(14)(23)\}$$
Show that for all $f \in K_4$ and all $h \in S_4$, we have $h^{-1}fh \in K_4$
I showed all the possible cycle shapes of h and am trying to show that $h^{-1}fh$ must always have cycle shape $(2,2)$...