Quadratic with complex rootsMediumQuestion 230015
Question
If z² + z + 1 = 0, then z equals:
- Aω or ω²Correct
- Bi or −i
- C1 or −1
- D0 or −1
Correct answer
ω or ω²
Explanation
z² + z + 1 = 0 → z = (−1 ± √(1−4))/2 = (−1 ± i√3)/2. These are precisely the non-real cube roots of unity ω and ω².