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Magazine Problem 14
Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ -36 i $$
Problem 14
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. $$ z_{1}=-1+i \sqrt{3}, z_{2}=\sqrt{3}+i $$
Problem 15
Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ -25 $$
Problem 15
Write each expression in terms of \(i\). $$\sqrt{-16}$$
Problem 16
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. $$ z_{1}=2 i, z_{2}=-5 i $$
Problem 16
Determine whether the graph of the given equation will be a line, circle, rose curve, lemniscate, cardioid, or lima莽on. Use Figures 15-21 to help you identify each equation, but do not actually sketch the graph.\(r=6\)
Problem 16
Write each expression in terms of \(i\). $$\sqrt{-64}$$
Problem 17
Write each expression in terms of \(i\). $$\sqrt{-121}$$
Problem 17
Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ 1+i \sqrt{3} $$
Problem 17
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. $$ -1-1+i,-2-4 i $$
