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:

Data Evaluating

The process of assessing or analyzing data to extract meaningful insights or to determine its reliability, relevance, and accuracy.

Hypnotic Analgesia

A technique through which hypnosis is used to reduce awareness of pain or diminish the sensation of pain.

Chronic Pain

Persistent pain that continues for weeks, months, or even years, beyond the usual course of an acute illness or healing of an injury.

Hypnosis Sessions

Sessions conducted by a trained therapist in which a person experiences deep relaxation and heightened focus, often used for therapeutic purposes.