# Euler's Formula
# Colorized Definition
\newcommand{\growth}{\color{c1}}
\newcommand{\rotation}{\color{c2}}
\renewcommand{\time}{\color{c3}}
\newcommand{\real}{\color{c4}}
\newcommand{\imaginary}{\color{c5}}
\newcommand{\location}{\color{c6}}
$$\growth e^{\rotation i \time x} \plain \location = \real \cos(x) \plain + \imaginary i\sin(x)$$
\growth Growth
\plain in a
\rotation perpendicular direction
\plain over
\time time
\\
\plain is circular:
\location here are the
\real horizontal
\\
\plain and
\imaginary vertical
\plain coordinates