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?
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 …
How do we compute Aut (Z2 x Z2)? - Mathematics Stack Exchange
Sep 26, 2015 · While computing Aut(Z4 ×Z2) =Z2 A u t (Z 4 × Z 2) = Z 2 and Aut(Z2 ×Z2 ×Z2) =S3 A u t (Z 2 × Z 2 × Z 2) = S 3, I considered all possible cases and checked if it was a …
How to get to the first step of solving $z^2=i$?
How do I get from z2 = i z 2 = i to z = x + iy z = x + i y? Is it a rule you use to solve the equation in general or specifically for this equation? (I don not understand the step from z2 = i z 2 = i to z …
Show that $|z+w|^2$ + $|z-w|^2$ = $2|z|^2 + 2|w|^2$
Jan 15, 2015 · @user146269 I used the identities $|z|^2 = z.\bar {z}$ and $\overline {z+w} = \bar {z}+\bar {w}$, which makes the proof shorter.
Proving that $\lim_ {z\to z_0}z^2+c=z_0^2+c$ - Mathematics …
Oct 4, 2020 · I am teaching myself complex analysis and after learning about epsilon-delta limits, I saw an exercise that asked to prove that $$\lim_ {z\to z_0}z^2+c=z_0^2+c$$ I would like to …
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 ...
What does $\\mathbb Z_2[x]$ means? - Mathematics Stack …
Jun 13, 2018 · I know Z2 Z 2 is the set of all integers modulo 2 2. But Z2[x] Z 2 [x] is the set of all polynomials. I am confused what it looks like.
Find all proper nontrivial subgroups of - Mathematics Stack …
Jan 19, 2014 · Find all proper nontrivial subgroups of Z2 × Z2 × Z2 Z 2 × Z 2 × Z 2 - Fraleigh p. 110 Exercise 11.10 Ask Question Asked 11 years, 11 months ago Modified 4 years, 6 months …
What means a set in $Z^2$? - Mathematics Stack Exchange
If B B is a proper subset of this, which is what B ⊂Z2 B ⊂ Z 2 means, then B B is some set whose elements are pairs of integers.