Finding an Orthornomal Polarization?

[Noone1982]

Say I have a polarization [3i, 2], How do I find a polarization that is orthogonal?

I know that,

$$AA^{\cdot }\; +\; BB^{\cdot }\; =\; 0$$

But my problem is that it yields one equation and two unknowns which I can't solve for. Furthermore, I am a bit confused on the representation of [3i,2] I understand [1,(+/-)i] is circularly polarized light but what about when the i is atop?

 

[Mindscrape]

So, you know that something is orthogonal when its inner product is zero. Find all A' and B' such that this the condition is satisfied. Even though you have one equation and two unknowns, that just indicates that there are infinite solutions depending on a free variable.

You are confused on the mathematical representation or the physical representation?