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Write each expression in terms of \(i\). $$\sqrt{-225}$$

Find the two square roots for each of the following complex numbers. Write your answers in standard form. $$ 1-i \sqrt{3} $$

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. $$ z_{1}=1+i, z_{2}=3 i $$

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. $$ z_{1}=-5, z_{2}=1+i \sqrt{3} $$

Find the three cube roots for each of the following complex numbers. Leave your answers in trigonometric form. $$ 8\left(\cos 210^{\circ}+i \sin 210^{\circ}\right) $$

Write each expression in terms of \(i\). $$\sqrt{-18}$$

Write each expression in terms of \(i\). $$\sqrt{-48}$$

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. $$ z_{1}=-3, z_{2}=\sqrt{3}+i $$

Find the three cube roots for each of the following complex numbers. Leave your answers in trigonometric form. $$ 27\left(\cos 303^{\circ}+i \sin 303^{\circ}\right) $$

Write each expression in terms of \(i\). $$\sqrt{-8}$$