A-11.3 Euler’s Formula

The value of $e^{\mathit{𝑖𝜃}}$ is represented as a coordinate on a circle in the complex plane in Figure 3, where the $x$-axis encodes the value’s real number part and the $y$-axis encodes the value’s imaginary number part. Note that as $𝜃$ increases, the complex part oscillates between $i$ and $-i$, and the real part oscillates between $1$ and $-1$, with the period of $2\pi$.