Question

Find the quotient of the complex numbers. Leave answer in polar form.

z1=1/8(cos2pi/3 + i sin2pi/3)
z2=1/3(cospi/4 + i sinpi/4)

(answer choices are in the image below)

Answer 1

`\bf \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[cos(\alpha)+isin(\alpha)]}{r_2[cos(\beta)+isin(\beta)]}\implies \cfrac{r_1}{r_2}[cos(\alpha - \beta)+isin(\alpha - \beta)]\\\\ -------------------------------`


`\bf \cfrac{z1}{z2}\implies \cfrac{(1)/(8)\left[cos\left((2\pi )/(3) \right)+i~sin\left((2\pi )/(3) \right) \right]} {(1)/(3)\left[cos\left((\pi )/(4) \right)+i~sin\left((\pi )/(4) \right) \right]} \\\\\\ \cfrac{\quad (1)/(8)\quad }{(1)/(3)}\left[cos\left((2\pi )/(3)-(\pi )/(4) \right)+i~sin\left((2\pi )/(3)-(\pi )/(4) \right) \right] \\\\\\ \cfrac{3}{8}\left[cos\left((5\pi )/(12) \right)+i~sin\left((5\pi )/(12) \right) \right]`