I need to implement some pricing functions which involve complex numbers. The equations involve various expressions such as $Re$ and $Img$ (i.e the real and imaginary part of the complex number), and I need to do some Fast Fourier Transforms and other things. Obviously the end result is always real, but the intermediate calculations are complex.
I have never used complex numbers before when I have programmed, so is there something particular I should be aware of? I want to use either R or C++: which would be more suitable for handling complex numbers? Are there any computational difficulties when dealing with complex numbers?