91Ó°ÊÓ

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. $$ r^{2} \sin ^{2} \theta+2 r \cos \theta=3 $$

$$ \text { For Exercises 65-76, simplify and express in standard form. } $$ $$ i^{40} $$

$$ \text { For Exercises 65-76, simplify and express in standard form. } $$ $$ i^{18} $$

In Exercises 63-74, find all complex solutions to the given equations. $$ x^{6}+1=0 $$

In Exercises 61-72, use a calculator to express each complex number in rectangular form. $$ 2\left[\cos \left(\frac{4 \pi}{7}\right)+i \sin \left(\frac{4 \pi}{7}\right)\right] $$

Consider the parametric equations \(x=a \sin (a t)-\sin t\) and \(y=a \cos (a t)-\cos t\). Use a graphing utility to explore the graphs for \(a=2\) and 3 . If \(y=a \cos (a t)+\cos t\), explore the graphs for \(a=2\) and 3 . Describe the \(t\)-interval for a complete cycle for each case.

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. $$ r^{2} \cos ^{2} \theta+r \sin \theta=3 $$

In Exercises 61-72, use a calculator to express each complex number in rectangular form. $$ -2\left[\cos \left(\frac{3 \pi}{5}\right)+i \sin \left(\frac{3 \pi}{5}\right)\right] $$

In Exercises 63-74, find all complex solutions to the given equations. $$ x^{6}-1=0 $$

$$ \text { For Exercises 65-76, simplify and express in standard form. } $$ $$ (5-2 i)^{2} $$