1. The problem statement, all variables and given/known data http://www-thphys.physics.ox.ac.uk/people/JamesBinney/complex.pdf Example 1.2 (Page 6) 2. Relevant equations De Moivre's Theorem, Euler's Formula, and other simple complex number theory formulas 3. The attempt at a solution I'm having troubles understanding the format, which makes me thing the author is assuming prior knowledge in another area of math. What I don't understand is where he gets the mSYMBOL format from. I don't know what that symbol is, so I couldn't google it. I get all of the simplifying, except for when the conversion happens to and from the mSYMBOL. It looks like he's simply converting the sin(2n + 1) to the complex exponential function, but how can you do that without i? I know sin(n) = 1/(2i) * (e^(in)-e^(-in)), but that's not even close to the result they got. If that's the case, then my question is, how is this transformation happening? Again, I understand the simplifying of the series, just not the transformation to and from the complex exponential. Hopefully I explained that well enough. Any help would be appreciated.