Polar form Multiplication

Last updated Mar 6, 2022 Edit Source

• Math calculus

Multiplying in Polar Coordinates causes a bunch of shit to go haywire. Here are some rules: for two given polar points $z = r(cos(\theta)+isin(\theta))$ and $w = s(cos(\phi)+isin(\phi))$

• $zw = rs(cos(\theta + \phi)+isin(\theta + \phi))$
• $\frac{z}{w} = \frac{r}{s}(cos(\theta - \phi)+isin(\theta - \phi))$
• $z^n = r^n(cos(n\theta)+isin(n\theta))$