If that were the definition, then we run into troubles, because (-i)^2=-1 as well...

When you introduce complex numbers, you can define them as a pair of real numbers (a,b) with actions:

(a,b)+(c,d)=(a+c,b+d),

(a,b)*(c,d)=(ac-db,ad+bc).

Then i is defined as a pair (0,1) and from the * definition it follows that (0,1)*(0,1)=(-1,0).

Now if you think of a pair (a,b) as a+ib (that notation requires some care, but only from formal point of view), then i^2=-1.

So i^2=-1 is not a definition, it's a property.

About the OP. There's an old joke.

i and pi talks.

pi: get real.

i: get rational.