Problem
\[ 32\left(\cos 60^{\circ}+i \sin 60^{\circ}\right) \] Next, using DeMoivre's find the 5 th root of \[ \begin{array}{c} 16+16 \sqrt{3} i= \\ 32\left(\cos 60^{\circ}+i \sin 6.0^{\circ}\right) \end{array} \] Find \( r \) and \( \theta \) where \( \theta \) is in the third quadrant. \[ \begin{array}{c} r^{5}=32 \\ 5 \theta=60^{\circ}, 420^{\circ}, 780^{\circ}, 1140^{\circ}, 1500^{\circ} \\ r=2 \quad \theta=[?] \circ \end{array} \] Enter
Solution
Step 1 ：\( r = 2 \)
Step 2 ：\( 5\theta = 60^{\circ}, 420^{\circ}, 780^{\circ}, 1140^{\circ}, 1500^{\circ} \)
Step 3 ：\( \theta = 240^{\circ} \)
