Taking a sum of exponentials and turning it into a fraction I'm curious as to how they made this jump in logic:
$$A e^{i \omega t} \left[1 + e^{i \phi} + e^{2i\phi} + \dots + e^{(N-1)i\phi}\right] = A e^{i\omega t} \frac{e^{i N\phi} - 1}{e^{i\phi} - 1}$$
How did they convert the sum within the brackets into the expression below? 

They used:
 1. Power laws: $(e^x)^a=e^{xa}$
 2. The sum of a geometric series
