91Ó°ÊÓ

Find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$z_{1}=9\left[\cos \left(\frac{5 \pi}{12}\right)+i \sin \left(\frac{5 \pi}{12}\right)\right] \text { and } z_{2}=3\left[\cos \left(\frac{\pi}{12}\right)+i \sin \left(\frac{\pi}{12}\right)\right]$$

Convert each point to exact polar coordinates. Assume that \(0 \leq \theta<2 \pi.\) $$(3,0)$$

Perform the indicated vector operation, given \(u=(-4,3)\) and \(v=\langle 2,-5\rangle\) $$\mathbf{u}+\mathbf{v}$$

Express each complex number in polar form. $$3+0 i$$

Express each complex number in polar form. $$-2+0 i$$

Perform the indicated vector operation, given \(u=(-4,3)\) and \(v=\langle 2,-5\rangle\) $$u-v$$

Find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$z_{1}=8\left[\cos \left(\frac{5 \pi}{8}\right)+i \sin \left(\frac{5 \pi}{8}\right)\right] \text { and } z_{2}=4\left[\cos \left(\frac{3 \pi}{8}\right)+i \sin \left(\frac{3 \pi}{8}\right)\right]$$

Find the angle (round to the nearest degree) between each pair of vectors. $$\langle 1,5\rangle \text { and }\langle-3,-2\rangle$$

Convert each point to exact polar coordinates. Assume that \(0 \leq \theta<2 \pi.\) $$(-7,-7)$$

Find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$z_{1}=45\left[\cos \left(\frac{22 \pi}{15}\right)+i \sin \left(\frac{22 \pi}{15}\right)\right] \text { and } z_{2}=9\left[\cos \left(\frac{2 \pi}{15}\right)+i \sin \left(\frac{2 \pi}{15}\right)\right]$$