How do I do this? Complex number question with magnitude

Question

X^3+1=0

Solve the equation over the set of complex numbers, find the magnitude of the solutions.

Answer 1

I would start by factoring it as a sum of cubes.

x³ + 1 = (x + 1)(x² - x + 1) = 0

You can see from the factor (x + 1) that -1 is a real solution. Now get the two complex solutions from the factor (x² - x + 1) using the quadratic formula.

x = [1 ± √(-3)]/2

x = (1 ± i√3)/2 = 1/2 ± i[(√3)/2]

|x| = {(1/2)² + [(√3)/2]²}^1/2 = ?

You can finish from here.