Final answer:
To find the complex fifth roots of (5 - 5√3i), we convert it to polar form and calculate the roots using the formula for de Moivre's Theorem. However, without proper clarification on the question, generating an exact set of roots from the provided options is not possible.
Step-by-step explanation:
To find the complex fifth roots of (5 - 5√3i), we first convert the complex number into polar form, that is, r(cos θ + i sin θ) or re^{iθ}. The modulus r is the square root of the sum of the squares of the real and imaginary parts, which gives us √(5² + (5√3)²) = √(25 + 75) = √100 = 10. The angle θ, called the argument, is found using the arctangent of the imaginary part divided by the real part, θ = atan(-√3/1) which is -60° (or -π/3 radians). To find the fifth roots, we divide the angle by 5 and find five equidistant points on the circle of radius 10 in the complex plane. Therefore, the fifth roots are all of the form 10^(⅓)(cos(θ/5 + 2kπ/5) + i sin(θ/5 + 2kπ/5)) for k=0,1,2,3,4.
When we calculate these values, we'll obtain five different complex numbers which are approximate: (2, -1.732), (-2, -1.732), (-1.236, 1.618), (1.236, 1.618), and (0, 2). However, this question seems to carry typographical errors or is incomplete, and we cannot provide an accurate set of options without proper clarification.