next up previous contents
Next: Power Series Expansions Up: Complex Numbers and Harmonic Previous: Complex Numbers   Contents

Trigonometric and Exponential Relations


$\displaystyle e^{\pm i \theta}$ $\displaystyle =$ $\displaystyle \cos(\theta) \pm i \sin(\theta)$ (74)
$\displaystyle \cos(\theta)$ $\displaystyle =$ $\displaystyle \frac{1}{2} \left(e^{+i \theta} + e^{-i
\theta}\right)$ (75)
$\displaystyle \sin(\theta)$ $\displaystyle =$ $\displaystyle \frac{1}{2i} \left(e^{+i \theta} - e^{-i
\theta}\right)$ (76)

From these relations and the properties of exponential multiplication you can painlessly prove all sorts of trigonometric identities that were immensely painful to prove back in high school



Robert G. Brown 2011-04-19