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

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

• A. $z_1・z_2=15CiS\left(\frac{11\pi^2}{12}\right)$
• B. $z_1・z_2=15CiS\left(\frac{\pi}{2}\right)$
• C. $z_1・z_2=CiS\left(\frac{\pi^2}{2}\right)$
• D. $z_1・z_2=15CiS\left(\frac{11\pi}{12}\right)$

Given $z_1=\frac23\left(\cos25\degree+i\sin25\degree\right)$ and $z_2=\frac52\left(\cos15\degree+i\sin15\degree\right)$, find the product $z_1・z_2$.

• A. $z_1・z_2=\frac53CiS\left(375\degree\right)$
• B. $z_1・z_2=CiS\left(40\degree\right)$
• C. $z_1・z_2=\frac{19}{6}CiS\left(40\degree\right)$
• D. $z_1・z_2=\frac{19}{6}CiS\left(375\degree\right)$

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 $\frac{z_1}{z_2}$.

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

Given $z_1=12\left(\cos30\degree+i\sin30\degree\right)$ and $z_2=3\left(\cos50\degree+i\sin50\degree\right)$, find the quotient $\frac{z_1}{z_2}$.

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