We’re about to make one of the most profound links that we will obtain through complex numbers. This is going to show how complex numbers are a bridge between different areas that you already know about, but never knew had anything to do with one another.
We know about exponential functions and how they have very special properties related to their derivatives. is a function which is practically defined as the function which is equal to its derivative. We also know that exponential functions tell us about growth, and we will see this in more detail when we come on to differential equations.
We know that trigonometric functions are to do with triangles, and circles, and angles and they tend to be periodic. They tell us how things vary in a way where they come back to where they started after some time.
Exponential functions and trigonometric functions couldn’t really look much more different if they tried.…