Lecture 2 - Math Review

• Get the Schaums math reference
  • Differential equations section is good
  • Can use it during exams

Complex Numbers

A complex number can be represented by the following

$$\tilde{z}=a+jb$$

Using Euler’s equation you can represent a complex number as

$$r(\cos \theta +j\sin \theta )=r{e}^{j\theta }$$

with

$$r=\sqrt{\vec{r}\cdot \vec{r}}=\sqrt{x^2+y^2}$$ $$\theta =\arctan \frac{c+d}{a+b}$$ $$\tilde{z}=r{e}^{i\theta }$$

Phasors represent harmonic quantities Manipulating Complex ratios Class activity 2

Complex cosine function

$$\cos z=\frac{e^{iz}+e^{-iz}}{2}$$

Complex sine function

$$\sin z=\frac{e^{iz}+e^{-iz}}{2i}$$

De-broglie wavelength

already knew a good bit of this stuff… fill in if you want