Just returned with a meeting with my supervisor. After several months of no-progress, we are back on track. Hooray!
For Chao0s: Using Euler\'s formula for complex numbers (recall for some complex number z, if we take the modulus and the argument, we\'ve z=|z|e^(i*arg(z))), we know i=e^(i*pi/2).
So i^i=(e^(i*pi/2))^i
Using exponential laws (eg. (x^2)^3=e^(2*3)), we now have:
...=e^((i^2)*pi/2)=e^(-pi/2) which can be evaluated on your calculator and is a real number. (0.207879576...)
So that\'s that

If none of the above makes sense, try writing it down on paper without all the ^ and ()