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

question 190

Multiple Choice

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

• A) \( 1+0 \mathrm{i} \)
• \[
• \begin{array}{l}
• \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \\
• \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \\
• \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \\
• \cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i \\
• \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i \\
• \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} \\
• \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 \mathrm{i} \\
• 1-i
• \end{array}
• \]
• B) \( 1+0 \mathrm{i} \)
• \[
• \begin{array}{l}
• \cos \frac{\pi}{9}+i \sin \frac{\pi}{9} \approx 0.94+0.34 i \\
• \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \\
• \cos \frac{\pi}{3}+i \sin \frac{\pi}{3}=0.50+i \frac{\sqrt{3}}{2} \\
• \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \\
• \cos \frac{5 \pi}{9}+i \sin \frac{5 \pi}{9} \approx-0.17+0.98 i \\
• \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \\
• \cos \frac{7 \pi}{9}+i \sin \frac{7 \pi}{9} \approx-0.77+0.64 i \\
• \cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i
• \end{array}
• \]
• C) \( 1+0 i \)
• \( \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \)
• \( \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \)
• \( \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \)
• \( \cos \frac{8 \pi}{9}+i \sin \frac{8 \pi}{9} \approx-0.94+0.34 i \)
• \( \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i \)
• \( \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} \)
• \( \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i \)
• \( \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i \)
• D) \( 1+0 i \)
• \( \cos \frac{2 \pi}{9}+i \sin \frac{2 \pi}{9} \approx 0.77+0.64 i \)
• \( \cos \frac{4 \pi}{9}+i \sin \frac{4 \pi}{9} \approx 0.17+0.98 i \)
• \( \cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}=-0.50+i \frac{\sqrt{3}}{2} \)
• \( -1+0 i \)
• \( \cos \frac{10 \pi}{9}+i \sin \frac{10 \pi}{9} \approx-0.94-0.34 i \)
• \( \cos \frac{4 \pi}{3}+i \sin \frac{4 \pi}{3}=-0.50-i \frac{\sqrt{3}}{2} \)
• \( \cos \frac{14 \pi}{9}+i \sin \frac{14 \pi}{9} \approx 0.17-0.98 i \)
• \( \cos \frac{16 \pi}{9}+i \sin \frac{16 \pi}{9} \approx 0.77-0.64 i \)

---

Definitions:

Environment

The surroundings or conditions in which a person, animal, or plant lives or operates; including both natural and built environments.

Economically Disadvantaged

A term describing individuals or groups living in poverty or in financial situations that limit access to basic resources and opportunities.

Ambivalent Attachment

A form of insecure attachment where a child is overly dependent on caregivers and exhibits anxiety or distress when separated from them.

Avoidant Attachment

A type of insecure attachment style characterized by a tendency to maintain emotional distance from others and minimize close emotional ties.