# Question in section on rings and fields

• Mar 26th 2010, 12:56 AM
Zennie
Question in section on rings and fields
Consider the set of numbers $a + bi$ where $a$ and $b$ are elements of $\mathbb{Z}/2\mathbb{Z}$. $i^2 = -1$ which in $\mathbb{Z}/2\mathbb{Z}$ is the same as $1$. Write down all 4 elements of this set of numbers. Which elements have inverses?
• Mar 26th 2010, 01:16 AM
Swlabr
Quote:

Originally Posted by Zennie
Consider the set of numbers $a + bi$ where $a$ and $b$ are elements of $\mathbb{Z}/2\mathbb{Z}$. $i^2 = -1$ which in $\mathbb{Z}/2\mathbb{Z}$ is the same as $1$. 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 $a+ib$ where $a$ and $b$ are either 1 or 0?

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