Answer: (−1 ± i√3)/2.
- A (−1 ± i√3)/2
- B (1 ± i√3)/2
- C (−1 ± i√3)/3
- D ±i
Correct answer: A. (−1 ± i√3)/2
Explanation: Factor: x³-1=(x-1)(x²+x+1)=0. The non-real roots come from x²+x+1=0. Quadratic formula: x=(-1±√(1-4))/2=(-1±√(-3))/2=(-1±i√3)/2. These are the complex cube roots of unity ω and ω². Answer: (-1±i√3)/2
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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