91Ó°ÊÓ

Find the two square roots for each of the following complex numbers. Leave your answers in trigonometric form. In each case, graph the two roots. $$ 9\left(\cos 310^{\circ}+i \sin 310^{\circ}\right) $$

Sketch the graph of each equation by making a table using values of \(\theta\) that are multiples of \(45^{\circ}\).\(r=\cos 2 \theta\)

Use your graphing calculator in polar mode to generate a table for each equation using values of \(\theta\) that are multiples of \(15^{\circ}\). Sketch the graph of the equation using the values from your table.\(r=2 \sin 2 \theta\)

Find the two square roots for each of the following complex numbers. Leave your answers in trigonometric form. In each case, graph the two roots. $$ 49 \operatorname{cis} \pi $$

Multiply. Leave all answers in trigonometric form. $$ 2 \operatorname{cis} \frac{3 \pi}{4} \cdot 2 \operatorname{cis} \frac{\pi}{4} $$

Multiply. Leave all answers in trigonometric form. $$ 2 \operatorname{cis} \frac{2 \pi}{3} \cdot 4 \operatorname{cis} \frac{7 \pi}{6} $$

Find the two square roots for each of the following complex numbers. Leave your answers in trigonometric form. In each case, graph the two roots. $$ 81 \operatorname{cis} \frac{5 \pi}{6} $$

Use your graphing calculator in polar mode to generate a table for each equation using values of \(\theta\) that are multiples of \(15^{\circ}\). Sketch the graph of the equation using the values from your table.\(r=2 \cos 2 \theta\)

Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ 2+2 i \sqrt{3} $$

Match each power of \(i\) with its corresponding value when simplified. 2\. \(i^{1}\) b. \(i^{2}\) C. \(i^{3}\) d. \(i^{4}\) i. \(-1\) ii. 1 iii. \(i\) iv. \(-i\)