Generated by the Physics Derivation Graph. Eq. \ref{eq:1580045} is an initial equation. $$\exp(i x) = \cos(x)+i \sin(x) \label{eq:1580045}$$ Change variable $$x$$ to $$\pi$$ in Eq. \ref{eq:1580045}; yields Eq. \ref{eq:1148677}. $$\exp(i \pi) = \cos(\pi)+i \sin(\pi) \label{eq:1148677}$$ Simplify Eq. \ref{eq:1148677}; yields Eq. \ref{eq:8524301}. $$\exp(i \pi) = -1 + i 0 \label{eq:8524301}$$ Simplify Eq. \ref{eq:8524301}; yields Eq. \ref{eq:9610540}. $$\exp(i \pi) = -1 \label{eq:9610540}$$ Add $$1$$ to both sides of Eq. \ref{eq:9610540}; yields Eq. \ref{eq:9472905}. $$\exp(i \pi) + 1 = 0 \label{eq:9472905}$$ Eq. \ref{eq:9472905} is one of the final equations.