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Express the Indicated Roots of Unity in Standard Form a

Question 62

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


A) 1+0icosπ5+isinπ50.81+0.59icos2π5+isin2π50.31+0.95icos3π5+isin3π50.31+0.95icos4π5+isin4π50.81+0.59i\begin{array}{l}1+0 \mathrm{i} \\\cos \frac{\pi}{5}+\mathrm{i} \sin \frac{\pi}{5} \approx 0.81+0.59 \mathrm{i} \\\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 \mathrm{i} \\\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 \mathrm{i} \\\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 \mathrm{i}\end{array}

B) 1+0icos2π5+isin2π50.31+0.95icos4π5+isin4π50.81+0.59icos6π5+isin6π50.810.59icos8π5+isin8π50.310.95i\begin{array}{l}1+0 i \\\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 \mathrm{i} \\\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \\\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \\\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 \mathrm{i}\end{array}

C) cos2π5+isin2π50.31+0.95icos4π5+isin4π50.81+0.59icos6π5+isin6π50.810.59icos8π5+isin8π50.310.95icos12π5+isin12π50.31+0.95i\begin{array}{l}\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 \mathrm{i} \\\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 \mathrm{i} \\\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 \mathrm{i} \\\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 \mathrm{i} \\\cos \frac{12 \pi}{5}+i \sin \frac{12 \pi}{5} \approx 0.31+0.95 \mathrm{i}\end{array}

D) 1+0icos2π5+isin2π50.31+0.95icos4π5+isin4π50.81+0.59icos6π5+isin6π50.810.59icos8π5+isin8π50.310.95i\begin{array}{l}1+0 i \\\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \\\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \\\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \\\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i\end{array}

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