1.1 Complex Numbers and Complex Exponentials

We will describe harmonic oscillations and waves with complex exponentials as well as with sine and cosine functions.
See my review of complex numbers.
Exercise
Start with

$\begin{eqnarray*} z_1 &=& 1+i\\ z_2 &=& 3-2i \end{eqnarray*}$

(a) Express and in complex exponential form.
(b) Add them in Cartesian Form and sketch the operation on the complex plane.
(c) Multiply them in both Cartesian and complex exponential form and verify that you get the same each way.

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