Here's an equation I derived a long time ago:
where C is the constant of integration and i is the imaginary unit (you'll have to imagine the vertical lines for the absolute value of the fraction on the right-hand side of the equation).
The strangest thing I find about this equation is that i shows up on the right-hand side and not on the left-hand side (to check out the validity of this equation, differentiate both sides). So there's a type of crossover from the realm of real numbers to the realm of complex numbers.
Does anyone have an explanation as to what's really going on? That's my puzzle.