# 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 \$\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?
• Mar 26th 2010, 01:16 AM
Swlabr
Quote:

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.