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

question 189

Multiple Choice

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

• A) \( 1+0 \mathrm{i} \)
• \[
• \begin{array}{l}
• \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \\
• \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \\
• \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \\
• \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \\
• \cos \pi+i \sin \pi=-1+0 i \\
• \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \\
• \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \\
• \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \\
• \cos \frac{9 \pi}{5}+i \sin \frac{9 \pi}{5} \approx 0.81-0.59 i
• \end{array}
• \]
• B) \( 1+0 i \)
• \( \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \)
• \( \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \)
• \( 0+i \)
• \( \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \)
• \( \cos \pi+i \sin \pi=-1+0 i \)
• \( \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \)
• \( \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \)
• \( \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \)
• \( 0-i \)
• C) \( 1+0 i \)
• \[
• \begin{array}{l}
• \cos \frac{\pi}{10}+i \sin \frac{\pi}{10} \approx 0.95+0.31 i \\
• \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \\
• \cos \frac{3 \pi}{10}+i \sin \frac{3 \pi}{10} \approx 0.59+0.81 i \\
• \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \\
• \cos \frac{\pi}{2}+i \sin \frac{\pi}{2}=0+i \\
• \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \\
• \cos \frac{7 \pi}{10}+i \sin \frac{7 \pi}{10} \approx-0.59+0.81 i \\
• \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \\
• \cos \frac{9 \pi}{10}+i \sin \frac{9 \pi}{10} \approx-0.95+0.31 i
• \end{array}
• \]
• D) \( 1+0 i \)
• \( \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \)
• \( \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \)
• \( \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \)
• \( \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \)
• \( \cos \pi+i \sin \pi=-1+0 i \)
• \( \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \)
• \( \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \)
• \( \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \)
• \( 0-i \)

---

Definitions:

Group Development

The phases or stages that a group goes through as it forms, progresses, and matures in pursuit of its objectives.

Class Assignment

An instructional task given to students by their teacher which is to be completed during a defined period, either in class or as homework.

Group Development

The process through which a group evolves over time, including forming, storming, norming, performing, and adjourning stages.

Punctuated Equilibrium

A theory in evolutionary biology suggesting that species experience periods of significant changes (punctuations) in short timespans, separated by longer periods of stability (equilibrium).