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) \( 1+0 i \)
• \( \cos \frac{\pi}{5}+i \sin \frac{\pi}{5} \approx 0.81+0.59 i \)
• \( \cos \frac{2 \pi}{5}+i \sin \frac{2 \pi}{5} \approx 0.31+0.95 i \)
• \( \cos \frac{3 \pi}{5}+i \sin \frac{3 \pi}{5} \approx-0.31+0.95 i \)
• \( \cos \frac{4 \pi}{5}+i \sin \frac{4 \pi}{5} \approx-0.81+0.59 i \)
• \( \cos \pi+i \sin \pi=-1+0 i \)
• \( \cos \frac{6 \pi}{5}+i \sin \frac{6 \pi}{5} \approx-0.81-0.59 i \)
• \( \cos \frac{7 \pi}{5}+i \sin \frac{7 \pi}{5} \approx-0.31-0.95 i \)
• \( \cos \frac{8 \pi}{5}+i \sin \frac{8 \pi}{5} \approx 0.31-0.95 i \)
• \( 0-i \)

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Definitions:

Continuously Running IV

An intravenous line that delivers fluids, medication, or nutrition without interruption.

Over-The-Needle Catheter (ONC)

A medical device used to access veins for the delivery of medications or fluids, consists of a needle with a catheter sheathed over it.

Electronic Infusion Device (EID)

A medical device used to deliver fluids, such as nutrients and medications, into a patient's body in precise amounts.

Peripherally Inserted Central Catheter (PICC)

A long, thin tube inserted through a peripheral vein, typically in the arm, extending to a central vein near the heart, used for long-term intravenous access.