Question

The amplitude of \( \sin \frac{\pi}{5} + i \left( 1 - \cos \frac{\pi}{5} \right) \) is:

• A. \( \frac{\pi}{5} \)
• B. \( \frac{2\pi}{5} \)
• C. \( \frac{\pi}{6} \)
• D. \( \frac{\pi}{4} \)

Hint:

The amplitude of a complex number is the modulus, found by taking the square root of the sum of the squares of the real and imaginary parts.

Answer 1

The Correct Option is C

Step 1: Find the amplitude.
The amplitude is the modulus of the complex number formed by the real and imaginary parts. After calculation, we find the amplitude to be \( \frac{\pi}{6} \).
Thus, the correct answer is (3).