Final answer:
The given question involves complex numbers expressed in trigonometric form. The expressions z = 2 (cos 120° + i sin 120°) and z = 8 (cos 330° + sin 330°) can be simplified by converting them into rectangular form.
Step-by-step explanation:
The given question involves complex numbers expressed in trigonometric form.
The expression z = 2 (cos 120° + i sin 120°) represents a complex number with a magnitude of 2 and an argument of 120°.
Similarly, z = 8 (cos 330° + i sin 330°) represents a complex number with a magnitude of 8 and an argument of 330°.
To simplify these expressions, we can convert them into rectangular form using the formulas:
cos θ + i sin θ = cos θ + sin θ i = a + bi
By applying this formula, we can rewrite the given expressions as:
z = 2(cos 120° + i sin 120°) = 2(−1/2 + (√3/2)i) = −1 + √3i
z = 8 (cos 330° + sin 330°) = 8(√(3)/2 − 1/2i) = 4√(3) − 4i