Powers of Complex Numbers

Submitted by vladimir.arzt on Sun, 08/25/2024 - 14:53

Project ID:

7200000055

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Question:

Match each power of a complex number with its corresponding result of exponentiation in algebraic form.

Questions Title:

Power of a Complex Number

Answers Title:

Result of Exponentiation

Question 1:

{(\cos \frac{5}{3} π + i \cdot \sin \frac{5}{3} π)}^{12}

Answer 1:

1

Question 2:

{(\cos \frac{7}{6} π + i \cdot \sin \frac{7}{6} π)}^{28}

Answer 2:

- \frac{1}{2} + i \cdot \frac{\sqrt{3}}{2}

Question 3:

{(\frac{\sqrt{2}}{2} - i \cdot \frac{\sqrt{2}}{2})}^{15}

Answer 3:

\frac{\sqrt{2}}{2} + i \cdot \frac{\sqrt{2}}{2}

Question 4:

{(\cos \frac{3}{4} π + i \cdot \sin \frac{3}{4} π)}^{- 7}

Answer 4:

- \frac{\sqrt{2}}{2} + i \cdot \frac{\sqrt{2}}{2}

Question 5:

{(\cos \frac{5}{6} π + i \cdot \sin \frac{5}{6} π)}^{- 45}

Answer 5:

$i$

Question 6:

{(\cos \frac{π}{4} + i \cdot \sin \frac{π}{4})}^{22}

Answer 6:

- i

Answer 7:

\frac{\sqrt{3}}{2} - i \cdot \frac{1}{2}

Answer 8:

- \frac{\sqrt{3}}{2} + i \cdot \frac{1}{2}

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