Question

let z1=2(cos(pi/5)+isin(pi/5)) and z2=8(cos(7pi/6)+isin(7pi/6)). How would I solve to get z1/z2? Thanks for any help!

Answer 1

\[z1 = 2(\cos(\frac{\pi}{5}) + isin(\frac{\pi}{5}))\]
\[z2 = 8(\cos(\frac{7\pi}{6}) + isin(\frac{7\pi}{6}))\]

this is easier in Euler identity form:
\[z1 = 2e^(i\frac{\pi}{5})\]
\[z2 = 8e^(i\frac{7\pi}{6})\]
\[\frac{2}{8} * e^(i(\frac{\pi}{5} - \frac{7\pi}{8}))\]
\[\frac{2}{8}e^(i(\frac{-27\pi}{40}))\]
\[\frac{2}{8}e^(i\frac{57\pi}{40})\]

Answer 2

Thanks! and there's this one that I dont get what to do with this. Its for the same problem but it tells me to solve this: