For the following exercise,

Evaluate each root.

Evaluate the cube root of $z$ when $z=32 \operatorname{cis}\left(\frac{2 \pi}{3}\right)$.

For the following exercise,

Evaluate each root.

Evaluate the square root of $z$ when $z=16 \operatorname{cis}\left(100^{\circ}\right)$.

For the following exercise,

Describe the graph of the set of parametric equations.

$x(t)=-t^2$ and $y(t)$ is linear

Find the measure of each angle in the triangle shown in as we discussed earlier. Round to the nearest tenth.

For the following exercise, plot the complex number in the complex plane.

$$6-2 i$$

For the following exercise,

Use the table feature in the graphing calculator to determine whether the graphs intersect.

$$\left\{\begin{array}{l}x_1(t)=3 t \\ y_1(t)=2 t-1\end{array}\right.$$

and

$$\left\{\begin{array}{l}x_2(t)=t+3 \\ y_2(t)=4 t-4\end{array}\right.$$

For the following exercise,

Evaluate each root.

Evaluate the cube root of $z$ when $z=27 \operatorname{cis}\left(240^{\circ}\right)$.

For the following exercise, evaluate each root.

Evaluate the square root of $z$ when $z=25 \operatorname{cis}\left(\frac{3 \pi}{2}\right)$.

For the following exercise,

Parameterize (write parametric equations for) each Cartesian equation by using $x(t)=a \cos t$ and $y(t)=b \sin t$. Identify the curve.

Parameterize the line from $(4,1)$ to $(6,-2)$ so that the line is at $(4,1)$ at $t=0$, and at $(6,-2)$ at $t=1$.

For the following exercise,

Graph the polar equation. Identify the name of the shape.

$$r=-\theta$$

For the following exercise,

Use the parametric equations for integers $a$ and $b$ : $x(t)=a \cos ((a+b) t) \quad y(t)=a \cos ((a-b) t)$

If the parametric equations $x(t)=t^2$ and $y(t)=6-3 t$ have the graph of a horizontal parabola opening to the right, what would change the direction of the curve?

For the following exercise,

Find the powers of each complex number in polar form.

Find $z^3$ when $z=3 \operatorname{cis}\left(\frac{5 \pi}{3}\right)$.

For the following exercise, evaluate each root.

Evaluate the cube root of $z$ when $z=64 \operatorname{cis}\left(210^{\circ}\right)$.

For the following exercise,

Graph the polar equation. Identify the name of the shape.

$$r=4 \sin (5 \theta)$$