What is (\frac{\sqrt{3}+i}{\sqrt{3}-i})^{3} equal to?
- A. -1 ✓
- B. 0
- C. 1
- D. 3
Correct Answer: A. -1
Explanation
Converting to polar form, \sqrt{3}+i = 2e^{i\pi/6} and \sqrt{3}-i = 2e^{-i\pi/6}. Their ratio is e^{i\pi/3}. Cubing this gives e^{i\pi} = -1.
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