Moivre 2

Find the cube roots of 125(cos 288° + i sin 288°).

Correct answer:

r =  5
α₁ =  96 °
α₂ =  216 °
α₃ =  336 °

Step-by-step explanation:

$r=\sqrt[3]{125}=5$

${\alpha }_1=288\mathrm{/}3+0\cdot 360\mathrm{/}3=96\text{°}$

${\alpha }_2=288\mathrm{/}3+1\cdot 360\mathrm{/}3=216\text{°}$

$$\begin{gathered} {\alpha }_3=288\mathrm{/}3+2\cdot 360\mathrm{/}3=336\text{° } \\ {z}_1=5(\cos 96+i\sin 96) \\ {z}_2=5(\cos 216\text{°}+i\sin 216\text{°}) \\ {z}_3=5(\cos 336\text{°}+i\sin 336\text{°}) \end{gathered}$$

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