No not at all. I is just something that behaves as if it is equivalent to negative one (that is, the additive inverse of the multiplicative identity) after combining it with itself in some way. We commonly call this multiplication. If such a thing comes with another operation called addition that behaves similarly to addition and multiplication (i.e. form a ring), then they will behave like i. Geometrically, multiplication by I can be seen as a 90deg rotation of a 2d vector. Complex numbers are simply 2-d coordinates (or rather, they are isomorphic to 2-d coordinates). Nothing special really. Easy to measure with a protractor and ruler.

In general there are many algebraic rings with an element that, when multiplied by itself, produces the additive inverse of the multiplicative identity.