Question in section on rings and fields

**Zennie** · March 26th 2010, 12:56 AM

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?

**Swlabr** · March 26th 2010, 01:16 AM

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.

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