A.1  Euler’s equation

where $x$ is given in radians. When $x=\pi$, it leads to the famous identity $e^{\mathit{j\pi }}=-1$. The value $e^{\mathit{jx}}$ can be interpreted as a complex number with magnitude one and angle $x$ rad. Hence, Eq. (A.1) represents the conversion of this complex number from the polar to the Cartesian form $\text{cos}<!--\; FUNCTION\; APPLICATION\; -->(x)+j\text{sin}<!--\; FUNCTION\; APPLICATION\; -->(x)$.

Using the fact that cosine and sine are even and odd functions, respectively, one can write $e^{-\mathit{jx}}=\text{cos}<!--\; FUNCTION\; APPLICATION\; -->(x)-j\text{sin}<!--\; FUNCTION\; APPLICATION\; -->(x)$ and using Eq. (A.1) obtain

and