Question

Prove that the inequality of an imaginary number cannot be shown.

Answer 1

i is one of the imaginary numbers. There is two basic inequality which signs are >, <.

As there are ≥, ≤ we need to prove equal sign too.

If we suppose i=√-1 can be shown, then there are three cases.

1. i>0
2. i=0
3. i<0

Solution: By using basic laws, we multiply i on both sides.

1. i×i>0 → -1>0 (FALSE)
2. i×i=0 → -1=0 (FALSE)
3. i×i>0 → -1>0 (FALSE)

All cases were false. Therefore, the statement "the inequality of an imaginary number can be shown" is contradicted.

Therefore, the inequality of an imaginary number cannot be shown.