91Ó°ÊÓ

In Exercises 45-60, express each complex number in exact rectangular form. $$ \frac{3}{2}\left[\cos \left(\frac{7 \pi}{6}\right)+i \sin \left(\frac{7 \pi}{6}\right)\right] $$

For Exercises 49-64, write each quotient in standard form. $$ \frac{1-i}{1+i} $$

In Exercises \(51-62\), find all \(n\)th roots of \(z\). Write the answers in polar form, and plot the roots in the complex plane. $$ \sqrt{3}-i, n=3 $$

In Exercises 57 and 58 , determine whether each statement is true or false. Curves given by equations in rectangular form have orientation.

In Exercises 45-68, graph each equation. In Exercises 63-68, convert the equation from polar to rectangular form first and identify the resulting equation as a line, parabola, or circle. $$ r=-2 \cos \theta $$

For Exercises 49-64, write each quotient in standard form. $$ \frac{3-i}{3+i} $$

In Exercises 45-60, express each complex number in exact rectangular form. $$ \frac{9}{5}\left[\cos \left(\frac{3 \pi}{2}\right)+i \sin \left(\frac{3 \pi}{2}\right)\right] $$

In Exercises \(51-62\), find all \(n\)th roots of \(z\). Write the answers in polar form, and plot the roots in the complex plane. $$ 4 \sqrt{2}+4 i \sqrt{2}, n=3 $$

In Exercises 45-68, graph each equation. In Exercises 63-68, convert the equation from polar to rectangular form first and identify the resulting equation as a line, parabola, or circle. $$ r=-3 \sin (3 \theta) $$

In Exercises 45-68, graph each equation. In Exercises 63-68, convert the equation from polar to rectangular form first and identify the resulting equation as a line, parabola, or circle. $$ r=4 \theta $$