Complex Numbers

Step 1: Understanding the roots of the equation.
The equation can be factored as . The roots of this equation are and the two roots of the quadratic equation . These roots are the cube roots of unity, which are: where is a primitive cube root of unity.

Step 2: Analyzing the options.
(A) This is , which is one of the solutions.
(B) is not a solution to the equation.
(C) is also not a solution.
(D) This is , the other solution to the equation.

Step 3: Conclusion.
The correct answer is

(A)

(D)