Powers and Roots of Complex Numbers

9000034301

Level: 
B
Find the solution set of the following equation in the set of complex numbers. \[ x^{3} - 1 = 0 \]
\(\{1,\ -\frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} ,\ -\frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)
\(\{1,\ -1 + \mathrm{i}\sqrt{3},\ -1 -\mathrm{i}\sqrt{3}\}\)
\(\{1,\ -\frac{1} {2} + \mathrm{i}\frac{\sqrt{3}} {2} \}\)
\(\{1,\ -\frac{1} {2} -\mathrm{i}\frac{\sqrt{3}} {2} \}\)