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

micromass

Quote by PlanckShift

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.

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.

Number Nine

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.

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.