Final answer:
Using De Moivre's Theorem, the value of n for which z^n = 1 with z = (cos 30° + i sin 30°) is 6 because 6 * 30° is a multiple of 360°.
Step-by-step explanation:
The student's question involves finding the value of n such that z^n equals 1, where z is given as z = (cos 30° + i sin 30°). To solve this, we can apply De Moivre's Theorem, which states that for any complex number in polar form z = r(cos θ + i sin θ) and any integer n, z^n = r^n(cos(nθ) + i sin(nθ)). Therefore, we need to find a multiple of 30 degrees that, when divided by 360, has a remainder of 0 degrees to satisfy the cosine and sine terms equaling 1 and 0, respectively. An example value for n is 6, as 6 × 30° = 180°, which is a multiple of 360 degrees. Thus, z^6 would be (cos(180°) + i sin(180°)), equalling 1, making the correct answer (a) 6.