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This is a test.

\[\begin{equation*} \begin{array}{lllll} e^{i\phi} &=& \cos \phi + i \sin \phi &\quad \mathrel{\#} \text{Euler's Formula} \\ &\Rightarrow& e^{i\pi} = \cos \pi + i \sin \pi &\quad \mathrel{\#} \text{set $\phi = \pi$} \\ &\Rightarrow& e^{i\pi} = -1 + i \cdot 0 &\quad \mathrel{\#} \text{$\cos \pi = -1$ and $\sin \pi = 0$} \\ &\Rightarrow& e^{i\pi} = -1 + 0 &\quad \mathrel{\#} i \cdot 0 = 0 \\ &\Rightarrow& e^{i\pi} = -1 &\quad \mathrel{\#} \text{simplify} \\ &\Rightarrow& e^{i\pi} +1 = 0 &\quad \mathrel{\#} \text{Euler's Identity} \end{array} \end{equation*}\]