Complex numbers - Why does i^2 = -1 ?
Ive always wondered how it is known that i squared is -1.
We know that i = -1^0.5 Using the rule (a^.5)^2 we get -1 as the answer...fine.
But if we use the rule:
Root A X Root B = Root(AB). Therefore, subtituting -1 we get Root -1 X Root -1 = Root(-1x-1)
= Root (1)
So how do mathmaticians know that i squared = -1 not 1?