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Express the Indicated Roots of Unity in Standard Form a 1+0i 1+0 \mathrm{i}

Question 2

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Express the indicated roots of unity in standard form a + bi.
-Cube roots of unity


A) 1+0i 1+0 \mathrm{i}
cosπ3+isinπ3=0.5+32icos2π3+isin2π3=0.5+32i\begin{array}{l}\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}=0.5+\frac{\sqrt{3}}{2} i \\\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.5+\frac{\sqrt{3}}{2} \mathrm{i}\end{array}

B) 1+0i 1+0 \mathrm{i}
cos2π3+isin2π3=0.5+32icos4π3+isin4π3=0.532i\begin{array}{l}\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.5+\frac{\sqrt{3}}{2} i \\\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.5-\frac{\sqrt{3}}{2} i\end{array}

C) 1+i 1+i
cos2π3+isin2π3=0.5+32icos4π3+isin4π3=0.532i\begin{array}{l}\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.5+\frac{\sqrt{3}}{2} i \\\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.5-\frac{\sqrt{3}}{2} i\end{array}

 D)  cosπ3+isinπ3=0.5+32icos2π3+isin2π3=0.5+32icos4π3+isin4π3=0.532i\begin{array}{l}\text { D) } \cos \frac{\pi}{3}+i \sin \frac{\pi}{3}=0.5+\frac{\sqrt{3}}{2} i \\\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.5+\frac{\sqrt{3}}{2} i \\\cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.5-\frac{\sqrt{3}}{2} i\end{array}

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