Graphical Representation of Euler's Formula (Wikipedia)
This is one of the main concepts my control systems class focuses on. It simplifies a lot of the math. This is accomplished by switching between cartesian coordinates and polar coordinates. There are to parts to the complex number, the real part (x-axis) and imaginary part (y-axis).
Most concepts that engineers learn in school were developed by Leonhard Euler or one of the Bernoulli family. Euler's Formula is one of the most important tools that an engineer can use. It shows the relationship between trig functions and exponential functions.
Most of his work was the development of infinitesimal calculus. The is is a fancy way of saying it is the study of continuous change with really small numbers. He taught Euler when is was a kid. Most of his sons became mathematicians.
He is the son of Johann Bernoulli. The aerodynamics class all aerospace engineer majors are required to take devoted to Bernoulli's Principle. The most important thing to remember about Bernoulli's Principle is that when velocity increases, then pressure decreases. This is the main concept for a wing in flight.
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