Mathematics: 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)

Find the quotient of the complex numbers. leave

Ответ:

marofthejt9089

09.01.2022

$\bf \qquad \textit{division of two complex numbers}
\\\\
\cfrac{r_1[cos(\alpha)+isin(\alpha)]}{r_2[cos(\beta)+isin(\beta)]}\implies
 \cfrac{r_1}{r_2}[cos(\alpha - \beta)+isin(\alpha - \beta)]\\\\
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$\bf \cfrac{z1}{z2}\implies \cfrac{\frac{1}{8}\left[cos\left(\frac{2\pi }{3} \right)+i~sin\left(\frac{2\pi }{3} \right) \right]}
{\frac{1}{3}\left[cos\left(\frac{\pi }{4} \right)+i~sin\left(\frac{\pi }{4} \right) \right]}
\\\\\\
\cfrac{\quad \frac{1}{8}\quad }{\frac{1}{3}}\left[cos\left(\frac{2\pi }{3}-\frac{\pi }{4} \right)+i~sin\left(\frac{2\pi }{3}-\frac{\pi }{4} \right) \right]
\\\\\\
\cfrac{3}{8}\left[cos\left(\frac{5\pi }{12} \right)+i~sin\left(\frac{5\pi }{12} \right) \right]$