\[
32\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)
\]
Next, find \( \theta \) 's for all 5 roots of \( 16+16 \sqrt{3} i \).
\[
\theta=60^{\circ},[?]^{\circ},[]^{\circ},[\quad]^{\circ},[\quad]^{\circ}
\]
Remember, to find the different \( \theta ' s \), add
\[
360^{\circ} \text { to } \theta
\]

Answer

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Answer

\begin{aligned} \theta_5 &= 60^{\circ} + 360^{\circ} \cdot \frac{4}{5} = 348^{\circ} \end{aligned}

Steps

Step 1 ：\begin{aligned} \theta_1 &= 60^{\circ} \end{aligned}

Step 2 ：\begin{aligned} \theta_2 &= 60^{\circ} + 360^{\circ} \cdot \frac{1}{5} = 132^{\circ} \end{aligned}

Step 3 ：\begin{aligned} \theta_3 &= 60^{\circ} + 360^{\circ} \cdot \frac{2}{5} = 204^{\circ} \end{aligned}

Step 4 ：\begin{aligned} \theta_4 &= 60^{\circ} + 360^{\circ} \cdot \frac{3}{5} = 276^{\circ} \end{aligned}

Step 5 ：\begin{aligned} \theta_5 &= 60^{\circ} + 360^{\circ} \cdot \frac{4}{5} = 348^{\circ} \end{aligned}