Simulation: Complex Math Parser

Introduction
In my project to build a SPICE program, I ran across a problem; I need to be able to perform complex math from strings.  This has already been done a thousand times before but finding a free, good parser isn't easy.  So I decided to do this myself.  This article will explain briefly the process I'm using to parse a complex math string.

Basic Process

1. First check the string for incorrect characters.  This can be done while performing step 2
2. Define every character in the string as a type (ie. 0=operator, 1=real number, 2=imaginary number, 3=left parenthesis, 4=right parenthesis).  Define this into a separate string.  The reason you do this is to take in different number types (real, imaginary, scientific notation, etc.)
3. Next separate the string into tokens to be evaluated separately.  The most open parenthesis should be it's own token. (ie. str = "2*2j+(20+2j)^12" will turn into tokens "@1*@2+@3^@4") This is only an example.  I doubt i'll have a string like this.
4. Evaluate each token by recursion through the same function until it outputs a complex number. (a custom class)
5. With a complex number for the tokens you can then evaluate in precedent order of functions.
6. Output complex number 

That's the quick and easy of it.  I have only completed steps 1 and 2 so far.  The rest will hopefully be completed in the week.  Hope this is helpful...