complex numbers - Why is $ |z|^2 = z z^* $? - Mathematics Stack …
May 9, 2014 · I've been working with this identity but I never gave it much thought. Why is $ |z|^2 = z z^* $ ? Is this a definition or is there a formal proof?
How do we compute Aut (Z2 x Z2)? - Mathematics Stack Exchange
Sep 26, 2015 · How do we compute Aut (Z2 x Z2)? Ask Question Asked 10 years, 3 months ago Modified 6 years, 2 months ago
Solving $z^2=\bar z$ - Mathematics Stack Exchange
Sep 10, 2015 · How did you get your solutions? That would almost surely help identify whatever you missed.
Constructing the $Z_2 \\times Z_2$ group table - Mathematics …
Aug 30, 2020 · In A. Zee's group theory book p. 47-49, he constructs the group table with four elements $\\{I,A,B,C\\}$ $\\begin{array}{c|cccc} & I & A & B & C ...
Prove that $\mathbb {Z}_2 \times \mathbb {Z}_2$ is not cyclic
Dec 16, 2019 · My attempt: $\mathbb {Z}_2 $ has elements of the form $\ {1,x\}$ and $\mathbb {Z}_2 \times \mathbb {Z}_2$ has elements of the form $\ { (1,1), (1,x), (x, 1), (x, x) \}$ order of …
Show that ${\\rm Aut}(Z_2 \\times Z_2) \\cong S_3$
$\mathbf {Z}_2 \times \mathbf {Z}_2$ is a 2-dimensinal vector space over $\mathbf {Z}_2$ and the automorphisms of a vector space correspond to invertible linear maps on that vector space. …
group theory - Find all proper nontrivial subgroups of $\mathbb …
Jan 19, 2014 · (1). I don't know what you mean by perfect, but it is correct. $ {\mathbb Z}_4$ has an element of order 4, and $ {\mathbb Z}_2^3$ hasn't, so no subgroup of $ {\mathbb Z}_2^3$ …
What does $\mathbb Z_2 [x]$ means? - Mathematics Stack Exchange
Jun 13, 2018 · I know $\mathbb {Z}_2$ is the set of all integers modulo $2$. But $\mathbb {Z}_2 [x]$ is the set of all polynomials. I am confused what it looks like.
complex numbers - Prove that $ |z_1-z_2|^2+|z_2-z_3|^2+|z_3 …
Dec 15, 2025 · Here's a geometrical proof, which I think is a lot cooler than tedious calculations. Note that the imaginary part condition translates to this: $$|z_1||z_2|\sin (\angle Z_1OZ_2) = …
Quotient group (Z4×Z6) /(<2,2>) is isomorphic to Z2×Z2?
Dec 3, 2023 · The question was asked that what group it's isomorphic to, I wrote reasoning that it's isomorphic to Z2×Z2, and not isomorphic to cyclic group Z4 since Z4 is cyclic and the …