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Magazine Problem 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. $$ r=2 \sin 2 \theta $$
Problem 6
Multiply. Leave all answers in trigonometric form. $$ 2 \operatorname{cis} \frac{2 \pi}{3} \cdot 4 \operatorname{cis} \frac{\pi}{6} $$
Problem 6
Write each expression in terms of \(i\). \(\sqrt{-45}\)
Problem 7
Find the product \(z_{1} z_{2}\) in standard form. Then write \(z_{1}\) and \(z_{2}\) in trigonometric form and find their product again. Finally, convert the answer that is in trigonometric form to standard form to show that the two products are equal. $$ z_{1}=1+i, z_{2}=-1+i $$
Problem 7
Write each expression in terms of \(i\). \(\sqrt{-8}\)
Problem 7
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. $$ r=3+3 \sin \theta $$
Problem 8
Write each expression in terms of \(i\). \(\sqrt{-20}\)
Problem 8
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. $$ r=3+3 \cos \theta $$
Problem 8
Find the product \(z_{1} z_{2}\) in standard form. Then write \(z_{1}\) and \(z_{2}\) in trigonometric form and find their product again. Finally, convert the answer that is in trigonometric form to standard form to show that the two products are equal. $$ z_{1}=1+i, z_{2}=2+2 i $$
Problem 8
Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ -2+2 i \vee 3 $$
