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

Question 189

Multiple Choice

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


A) 1+0i 1+0 \mathrm{i}
cosπ5+isinπ50.81+0.59icos2π5+isin2π50.31+0.95icos3π5+isin3π50.31+0.95icos4π5+isin4π50.81+0.59icosπ+isinπ=1+0icos6π5+isin6π50.810.59icos7π5+isin7π50.310.95icos8π5+isin8π50.310.95icos9π5+isin9π50.810.59i\begin{array}{l}\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \\\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \\\cos \frac{3 \pi}{5}+i \sin \frac{3 \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 \pi+i \sin \pi=-1+0 i \\\cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \\\cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \\\cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \\\cos \frac{9 \pi}{5}+i \sin \frac{9 \pi}{5} \approx 0.81-0.59 i\end{array}
B) 1+0i 1+0 i
cosπ5+isinπ50.81+0.59i \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i
cos2π5+isin2π50.31+0.95i \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i
0+i 0+i
cos4π5+isin4π50.81+0.59i \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i
cosπ+isinπ=1+0i \cos \pi+i \sin \pi=-1+0 i
cos6π5+isin6π50.810.59i \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i
cos7π5+isin7π50.310.95i \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i
cos8π5+isin8π50.310.95i \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i
0i 0-i
C) 1+0i 1+0 i
cosπ10+isinπ100.95+0.31icosπ5+isinπ50.81+0.59icos3π10+isin3π100.59+0.81icos2π5+isin2π50.31+0.95icosπ2+isinπ2=0+icos3π5+isin3π50.31+0.95icos7π10+isin7π100.59+0.81icos4π5+isin4π50.81+0.59icos9π10+isin9π100.95+0.31i\begin{array}{l}\cos \frac{\pi}{10}+i \sin \frac{\pi}{10} \approx 0.95+0.31 i \\\cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \\\cos \frac{3 \pi}{10}+i \sin \frac{3 \pi}{10} \approx 0.59+0.81 i \\\cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \\\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i \\\cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \\\cos \frac{7 \pi}{10}+i \sin \frac{7 \pi}{10} \approx-0.59+0.81 i \\\cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \\\cos \frac{9 \pi}{10}+i \sin \frac{9 \pi}{10} \approx-0.95+0.31 i\end{array}
D) 1+0i 1+0 i
cosπ5+isinπ50.81+0.59i \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i
cos2π5+isin2π50.31+0.95i \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i
cos3π5+isin3π50.31+0.95i \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i
cos4π5+isin4π50.81+0.59i \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i
cosπ+isinπ=1+0i \cos \pi+i \sin \pi=-1+0 i
cos6π5+isin6π50.810.59i \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i
cos7π5+isin7π50.310.95i \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i
cos8π5+isin8π50.310.95i \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i
0i 0-i

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