If x, y and z are the cube roots of unity, then what is the value of xy+yz+zx?
- A. 0 ✓
- B. 1
- C. 2
- D. 3
Correct Answer: A. 0
Explanation
The cube roots of unity are 1, \omega, \omega^2. We need to evaluate 1\cdot\omega + \omega\cdot\omega^2 + \omega^2\cdot 1 = \omega + \omega^3 + \omega^2. Since \omega^3 = 1 and 1 + \omega + \omega^2 = 0, the sum evaluates to 0.
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