Answer: z = ω or ω².
- A z = i or -i
- B z = -1
- C z = 1 or -1
- D z = ω or ω²
Correct answer: D. z = ω or ω²
Explanation: Quadratic formula: z=(-1±√(1-4))/2=(-1±√(-3))/2=(-1±i√3)/2. These are precisely ω and ω², the primitive complex cube roots of unity (since z²+z+1=0 is the minimal polynomial of ω). Answer: z = ω or z = ω²
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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