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## Hi, I m trying to find out, what is imaginary unit/number. i^2

 Quote by PlanckShift Definition of a field.
OK, you found the definition. Now read the definition. In particular:

 Similarly, for any a in F other than 0, there exists an element a−1 in F, such that a · a−1 = 1.
 But ε2 = 0 remember? Think about it. How do you find the inverse of a+bε? Rationalize the expression using ε2 = 0. Then find where the resulting expression is undefined.

 Quote by PlanckShift But ε2 = 0 remember? Think about it. How do you find the inverse of a+bε? Rationalize the expression using ε2 = 0. Then find where the resulting expression is undefined.
But where is the inverse of ε?
Hint: It's 1/ε, which you said was undefined. It doesn't have an inverse, so your structure isn't a field.