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

Question 295

Multiple Choice

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


A) 1+0i 1+0 \mathrm{i}
cosπ4+isinπ4=22+22i1i0i\begin{array}{l}\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} i \\1-i \\0-i\end{array}
B) 1+0i 1+0 i
cosπ2+isinπ2=0+i \cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i
cosπ+isinπ=1+0i \cos \pi+i \sin \pi=-1+0 i
cos3π2+isin3π2=0i \cos \frac{3 \pi}{2}+i \sin \frac{3 \pi}{2}=0-i
C) 1+0i 1+0 i
cosπ4+isinπ4=22+22i \cos \frac{\pi}{4}+i \sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} i
cosπ2+isinπ2=0+i \cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i
cos3π4+isin3π4=22+22i \cos \frac{3 \pi}{4}+i \sin \frac{3 \pi}{4}=-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} i
D) 1+0i 1+0 \mathrm{i}
cosπ2+isinπ2=0+icosπ+isinπ=1+0i1i\begin{array}{l}\cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i \\\cos \pi+i \sin \pi=-1+0 i \\1-i\end{array}

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