91Ó°ÊÓ

Write each complex number in trigonometric form, using degree measure for the argument. \(3+4 i\)

Use De Moivre's theorem to simplify each expression. Write the answer in the form \(a+\) bi. $$ \left[2\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)\right]^{3} $$

Perform the indicated operations and write your answers in the form \(a+\) bi, where \(a\) and \(b\) are real numbers. $$ i^{19} $$

Convert the rectangular coordinates of each point to polar coordinates. Use degrees for \(\theta\). $$ (4,4) $$

Use De Moivre's theorem to simplify each expression. Write the answer in the form \(a+\) bi. $$ \left[\sqrt{3}\left(\cos 210^{\circ}+i \sin 210^{\circ}\right)\right]^{4} $$

Graph the following pairs of parametric equations with the aid of a graphing calculator. These are uncommon curves that would be difficult to describe in rectangular or polar coordinates. $$x=\sin t, y=t^{2}$$

Find the indicated roots in the form \(a+\) bi. Check by graphing the roots in the complex plane. The cube roots of 8.

Perform the indicated operations and write your answers in the form \(a+\) bi, where \(a\) and \(b\) are real numbers. $$ i^{-4} $$

Convert the rectangular coordinates of each point to polar coordinates. Use degrees for \(\theta\). $$ (-2,2) $$

Graph the following pairs of parametric equations with the aid of a graphing calculator. These are uncommon curves that would be difficult to describe in rectangular or polar coordinates. $$x=t-\sin t, y=1-\cos t(\text { cycloid })$$