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

Answer

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Answer

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

Steps

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

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

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

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

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