91Ó°ÊÓ

In Exercises 1-20, graph the curve defined by the following sets of parametric equations. Be sure to indicate the direction of movement along the curve. $$ x=\sin t+1, y=\cos t-2, t \text { in }[0,2 \pi] $$

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=4\left[\cos \left(\frac{3 \pi}{8}\right)+i \sin \left(\frac{3 \pi}{8}\right)\right] \text { and } z_{2}=3\left[\cos \left(\frac{\pi}{8}\right)+i \sin \left(\frac{\pi}{8}\right)\right] $$

In Exercises \(11-20\), convert each point given in rectangular coordinates to exact polar coordinates. Assume \(0 \leq \theta<2 \pi\). $$ (-1,-\sqrt{3}) $$

In Exercises 13-40, perform the indicated operation, simplify, and express in standard form. $$ (3-7 i)+(-1-2 i) $$

In Exercises 13-28, express each complex number in polar form. $$ 1-i $$

In Exercises 13-28, express each complex number in polar form. $$ 2+2 i $$

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=6\left[\cos \left(\frac{2 \pi}{9}\right)+i \sin \left(\frac{2 \pi}{9}\right)\right] \text { and } z_{2}=5\left[\cos \left(\frac{2 \pi}{9}\right)+i \sin \left(\frac{2 \pi}{9}\right)\right] $$

In Exercises 1-20, graph the curve defined by the following sets of parametric equations. Be sure to indicate the direction of movement along the curve. $$ x=\tan t, y=1, t \text { in }-\frac{\pi}{4}, \frac{\pi}{4} $$

In Exercises 13-40, perform the indicated operation, simplify, and express in standard form. $$ (1+i)+(9-3 i) $$

In Exercises \(11-20\), convert each point given in rectangular coordinates to exact polar coordinates. Assume \(0 \leq \theta<2 \pi\). $$ (6,6 \sqrt{3}) $$