91Ó°ÊÓ

Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left[2\left(\cos 135^{\circ}+i \sin 135^{\circ}\right)\right]^{4}$$

For each point given in polar coordinates, state the quadrant in which the point lies if it is graphed in a rectangular coordinate system. (a) \(\left(5,135^{\circ}\right)\) (b) \(\left(2,60^{\circ}\right)\) (c) \(\left(6,-30^{\circ}\right)\) (d) \(\left(4.6,213^{\circ}\right)\)

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$\left(5,-60^{\circ}\right)$$

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$\left(-3,-210^{\circ}\right)$$

Find the cube roots of each complex number. Leave the answers in trigonometric form. Then graph each cube root as a vector in the complex plane. $$27\left(\cos 300^{\circ}+i \sin 300^{\circ}\right)$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t^{2}+2, y=t^{2}-4 ; \text { for } t \text { in }(-\infty, \infty)$$

Find the sum of each pair of complex numbers. Express your answer in rectangular form. Do not use a calculator. $$7+6 i, 3 i$$

Solve each triangle. \(a=28\) feet, \(b=47\) feet, \(c=58\) feet

Find the cube roots of each complex number. Leave the answers in trigonometric form. Then graph each cube root as a vector in the complex plane. $$-64$$

Find a rectangular equation for each curve and graph the curve. $$x=2+\sin t, y=1+\cos t ; \text { for } t \text { in }[0,2 \pi]$$