Given z1=15(cos⁡π2+isin⁡π2)z_1=\frac15\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)z1=51(cos2π+isin2π) and z2=5(cos⁡π5+isin⁡π5)z_2=5\left(\cos\frac{\pi}{5}+i\sin\frac{\pi}{5}\right)z2=5(cos5π+isin5π), find the quotient z1z2\frac{z_1}{z_2}z2z1.

z 1 z 2 = 1 25 C i S ( 3 π 10 ) \frac{z_1}{z_2}=\frac{1}{25}CiS\left(\frac{3\pi}{10}\right) z 2 z 1 = 25 1 C i S ( 10 3 π )

Table of contents

17. Graphing Complex Numbers

Products and Quotients of Complex Numbers

Multiple Choice

Given $z_1=\frac15\left(\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}\right)$ and $z_2=5\left(\cos\frac{\pi}{5}+i\sin\frac{\pi}{5}\right)$ , find the quotient $\frac{z_1}{z_2}$ .

$\frac{z_1}{z_2}=\frac{1}{25}CiS\left(\frac{3\pi}{10}\right)$

$\frac{z_1}{z_2}=\frac{1}{25}CiS\left(\frac{5\pi}{2}\right)$

$\frac{z_1}{z_2}=-\frac{24}{5}CiS\left(\frac{3\pi}{10}\right)$

$\frac{z_1}{z_2}=-\frac{24}{5}CiS\left(\frac52\right)$

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