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 $A$ ?