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. $$ x=3 \sin t, y=2 \cos t, t \text { in }[0,2 \pi] $$

In Exercises 1-12, write each expression as a complex number in standard form. If an expression simplifies to either a real number or a pure imaginary number, leave in that form. $$ -10-\sqrt{-144} $$

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

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=\sqrt{3}\left[\cos \left(\frac{\pi}{12}\right)+i \sin \left(\frac{\pi}{12}\right)\right] \text { and } z_{2}=\sqrt{27}\left[\cos \left(\frac{\pi}{6}\right)+i \sin \left(\frac{\pi}{6}\right)\right] $$

In Exercises 1-12, graph each complex number in the complex plane. $$ 4-\frac{5}{2} i $$

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=\sqrt{5}\left[\cos \left(\frac{\pi}{15}\right)+i \sin \left(\frac{\pi}{15}\right)\right] \text { and } z_{2}=\sqrt{5}\left[\cos \left(\frac{4 \pi}{15}\right)+i \sin \left(\frac{4 \pi}{15}\right)\right] $$

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. $$ x=\cos (2 t), y=\sin t, t \text { in }[0,2 \pi] $$

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

In Exercises 1-12, write each expression as a complex number in standard form. If an expression simplifies to either a real number or a pure imaginary number, leave in that form. $$ 7-\sqrt[3]{-125} $$

In Exercises 1-12, graph each complex number in the complex plane. $$ -\frac{47}{10}-\frac{19}{10} i $$