91Ó°ÊÓ

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

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

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

Convert each point to exact polar coordinates. Assume that \(0 \leq \theta<2 \pi.\) $$(-\sqrt{3},-1)$$

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

Express each complex number in polar form. $$\frac{1}{6}-\frac{1}{6} i$$

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

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

Find the quotient \(\frac{z_{1}}{z_{2}}\) and express it in rectangular form. $$z_{1}=22\left[\cos \left(\frac{11 \pi}{18}\right)+i \sin \left(\frac{11 \pi}{18}\right)\right] \text { and } z_{2}=11\left[\cos \left(\frac{5 \pi}{18}\right)+i \sin \left(\frac{5 \pi}{18}\right)\right]$$

Find the result of each expression using De Moivre's theorem. Write the answer in rectangular form. $$(-1+i)^{5}$$