If r ≠ 0 is rational and i is irrational, then r i is irrational?

Frank Day

Frank Day

Answered

2022-07-03

If r 0 is rational and i is irrational, then r i is irrational?

Answer & Explanation

amanhantmk

amanhantmk

Expert

2022-07-04Added 17 answers

We only need to know that the rationals form a field: Suppose that r i is rational (i.e. r i Q )then i = r i r Q because we can divide a rational by a non-zero rational and the result is rational. But i is given not to be rational. This contradiction shows r i is not rational, so irrational.

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