2
$\begingroup$

Let $j=e^{2i\pi/3}$. How can I prove that the set $A=\mathbb{Z}+j\mathbb{Z}$ is stable under multiplication and conjugaison ? If I understood the question well, I need to prove the following :

a)If $x$ and $y$ are two elements of $A$, then $xy$ is also an element of A.

b)If $x$ is an element of $A$, so is $\bar x$.

For a), I tried basic multiplication stuff but could'nt write the result as $a+bj$ with $a$ and $b$ integers. And similarly for b).

And another problem I would like to solve is to find all inversible elements of $A$ ?

  • 0
    What exactly do you mean by "inversible elements of $A$"?2012-01-11
  • 0
    We say that $z$ is inversible in $A$ iff there exists $z^' \in A$ such that $zz^'=1$, i.e iff $\frac{1}{z} \in A$.2012-01-11

1 Answers 1