Originally Posted by

**habsfan31** In F9 = Z/3Z, there is no solution of the equation x^2 = −1, just as in R. So “invent”

a solution, call it 'i'. Then 'i' is a new “number” which satisfies i^2 = −1. Consider

the set F9[i] consisting of all numbers a+bi, with a,b in F9. Add and multiply these

numbers as though they were polynomials in 'i', except whenever you get i^2 replace

it by −1.

(i) Write down the nine elements of F9[i] .

(ii) Show that every nonzero element of F9[i] has an inverse, so that F9[i] is a

field.

I know im supposed to show you that ive tried the question if i want an answer. Believe me, i have tried it. Im just really confused by the wording of the question and am not really sure what they are looking for in part a. Once i get part a, im pretty sure id be able to get part b on my own.

Thanks