# Thread: Question in section on rings and fields

1. ## Question in section on rings and fields

Consider the set of numbers $\displaystyle a + bi$ where $\displaystyle a$ and $\displaystyle b$ are elements of $\displaystyle \mathbb{Z}/2\mathbb{Z}$. $\displaystyle i^2 = -1$ which in $\displaystyle \mathbb{Z}/2\mathbb{Z}$ is the same as $\displaystyle 1$. Write down all 4 elements of this set of numbers. Which elements have inverses?

2. Originally Posted by Zennie
Consider the set of numbers $\displaystyle a + bi$ where $\displaystyle a$ and $\displaystyle b$ are elements of $\displaystyle \mathbb{Z}/2\mathbb{Z}$. $\displaystyle i^2 = -1$ which in $\displaystyle \mathbb{Z}/2\mathbb{Z}$ is the same as $\displaystyle 1$. Write down all 4 elements of this set of numbers. Which elements have inverses?
What do you think the elements of the set are? What numbers are of the form $\displaystyle a+ib$ where $\displaystyle a$ and $\displaystyle b$ are either 1 or 0?

To find out which elements have inverses, square each element and see what happens.