Dimensional aspects of the imaginary unit $i$ in physics From a real world perspective each dimension in the 3-D Cartesian System can be represented by an axis that is perpendicular to 2 other axes. I read somewhere else that the effect of ${i}$ is to reorient data 90 degrees on the "imaginary" axis. I guess my question is this: What role ( if any)   does $i$ serve in everyday or even quantum physics?
${Edit}$
To clarify, I am more concerned with the dimensional aspects of $i$. If for instance you were to consider a 3-D location to be a "point" with length width and height in a complex graph representation with three additional mutually perpendicular axes? 
PS. I know this thread is getting a bit hair brained. But in my defense, I did look for a "specualation" tag before I posted this thread here.
$EDIT$
I changed $\sqrt{-1}$ back to $i$, because I am concerned with the hypothetical real world effect of the entity. Not the mathematical representation.
 A: What you're talking about seems to be (or at least lead to) Wick rotation which leads to all sort of crazy dualities between, for example, quantum and thermal physics or Minkowski and Euclidean geometries.
A: Firstly, you're referring to geometry on the 2D plane. Represent every point on your 2-plane by a position vector from an origin. The 2D (Real) plane is (in some very useful ways) equivalent to the Complex plane, which can be seen from the formula that any complex number can be written in two equivalent forms
$$x + \mathbf{i} y \equiv r e^{i \phi}$$
The format on the left is like using cartesian coordinates on the plane, while the format on the right is like using polar coordinates on the plane -- with $r = \sqrt{x^2 + y^2}$ and $\phi = \arctan{\frac{y}{x}}$, as usual.
One can show that multiplying any position vector by a Real number is akin to "scaling" the size of this position vector, but leaving invariant the direction in which it is pointing. One can also show that multiplying by some kinds of imaginary numbers (unimodular numbers of the form $e^{\mathbf{i} \phi}$) is like rotating them.
On the other hand, for 3D space, there is no such simple analogy to complex numbers. However, one could use quaternions (generalization of complex numbers) but that's more involved.
