91Ó°ÊÓ

For the following exercises, find the powers of each complex number in polar form. Find \(z^{4}\) when \(z=2 \operatorname{cis}\left(70^{\circ}\right)\)

For the following exercises, find the powers of each complex number in polar form. Find \(z^{2}\) when \(z=5 \operatorname{cis}\left(\frac{3 \pi}{4}\right)\)

For the following exercises, evaluate each root. Evaluate the cube root of \(z\) when \(z=64 \operatorname{cis}\left(210^{\circ}\right)\) .

For the following exercises, evaluate each root. Evaluate the square root of \(z\) when \(z=25 \operatorname{cis}\left(\frac{3 \pi}{2}\right)\) .

For the following exercises, plot the complex number in the complex plane. $$6-2 i$$

For the following exercises, plot the complex number in the complex plane. $$-1+3 i$$

For the following exercises, eliminate the parameter \(t\) to rewrite the parametric equation as a Cartesian equation. $$\left\\{\begin{array}{l}{x(t)=3 t-1} \\ {y(t)=\sqrt{t}}\end{array}\right.$$

For the following exercises, eliminate the parameter \(t\) to rewrite the parametric equation as a Cartesian equation. $$\left\\{\begin{array}{l}{x(t)=-\cos t} \\ {y(t)=2 \sin ^{2} t}\end{array}\right.$$

For the following exercises, eliminate the parameter \(t\) to rewrite the parametric equation as a Cartesian equation. Parameterize (write a parametric equation for) each Cartesian equation by using \(x(t)=a \cos t\) and \(y(t)=b \sin t\) for \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\).

For the following exercises, eliminate the parameter \(t\) to rewrite the parametric equation as a Cartesian equation. Parameterize the line from \((-2,3)\) to \((4,7)\) so that the line is at \((-2,3)\) at \(t=0\) and \((4,7)\) at \(t=1\).