Question

The value of \[ \left( \frac{1 + \cos\left(\frac{\pi}{12}\right) + i\sin\left(\frac{\pi}{12}\right)} {1 + \cos\left(\frac{\pi}{12}\right) - i\sin\left(\frac{\pi}{12}\right)} \right)^{72} \] is equal to: 

• A. \( 0 \)
• B. \( -1 \)
• C. \( 1 \)
• D. \( \frac{1}{2} \)
• E. \( -\frac{1}{2} \)

Hint:

Any expression of the form \( \left( \frac{1+\text{cis}\theta}{1+\text{cis}(-\theta)} \right) \) is simply \( \text{cis}\theta \). Recognizing this identity saves you from tedious rationalization of complex denominators.

Answer 1

The Correct Option is C