Euler's Formula

Colorized Definition

Euler's Formula

\newcommand{\growth}{\color{c1}}
\newcommand{\rotation}{\color{c2}}
\renewcommand{\time}{\color{c3}}
\newcommand{\real}{\color{c4}}
\newcommand{\imaginary}{\color{c5}}
\newcommand{\location}{\color{c6}}

\displaystyle{\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
## Read More - [Intuitive Understanding of Euler's Formula](https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/)

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