I feel ashamed asking this, but how do you take the integral of a complex or pure imaginary function? My sheer guess is that you take the real parts of the function and integrate them seperately, then take the imaginary part and integrate it, but I don't quite know how to do that last part. Also, can the definite integral of a complex or imaginary function ever be a real number? Does any function have a derivative or integral of i? And just to finish this up, is i positive or negative?