Products and Quotients of Complex Numbers - Video Tutorials & Practice Problems

Given $z_1=5(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6})$ and $z_2=3(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4})$, find the product $z_1\text{・}{z}_2$.

• A. $z_1\text{・}{z}_2=15CiS\left(\frac{11{\pi }^2}{12}\right)$
• B. $z_1\text{・}{z}_2=15CiS\left(\frac{\pi }{2}\right)$
• C. $z_1\text{・}{z}_2=CiS\left(\frac{{\pi }^2}{2}\right)$
• D. $z_1\text{・}{z}_2=15CiS\left(\frac{11\pi }{12}\right)$

Given $z_1=\frac{2}{3}(\cos 25°+i\sin 25°)$ and $z_2=\frac{5}{2}(\cos 15°+i\sin 15°)$, find the product $z_1\text{・}{z}_2$.

• A. $z_1\text{・}{z}_2=\frac{5}{3}CiS\left(375°\right)$
• B. $z_1\text{・}{z}_2=CiS\left(40°\right)$
• C. $z_1\text{・}{z}_2=\frac{19}{6}CiS\left(40°\right)$
• D. $z_1\text{・}{z}_2=\frac{19}{6}CiS\left(375°\right)$

Given $z_1=\frac{1}{5}(\cos \frac{\pi }{2}+i\sin \frac{\pi }{2})$ and $z_2=5(\cos \frac{\pi }{5}+i\sin \frac{\pi }{5})$, find the quotient $\frac{z_1}{z_2}$.

• A. $\frac{z_1}{z_2}=\frac{1}{25}CiS\left(\frac{3\pi }{10}\right)$
• B. $\frac{z_1}{z_2}=\frac{1}{25}CiS\left(\frac{5\pi }{2}\right)$
• C. $\frac{z_1}{z_2}=-\frac{24}{5}CiS\left(\frac{3\pi }{10}\right)$
• D. $\frac{z_1}{z_2}=-\frac{24}{5}CiS\left(\frac{5}{2}\right)$

Given $z_1=12(\cos 30°+i\sin 30°)$ and $z_2=3(\cos 50°+i\sin 50°)$, find the quotient $\frac{z_1}{z_2}$.

• A. $\frac{z_1}{z_2}=4CiS\left(20°\right)$
• B. $\frac{z_1}{z_2}=9CiS\left(340°\right)$
• C. $\frac{z_1}{z_2}=9CiS\left(20°\right)$
• D. $\frac{z_1}{z_2}=4CiS\left(340°\right)$