Answer: 2.
- A 2
- B 4
- C 6
- D 8
Correct answer: A. 2
Explanation: Let t = 2<sup>1/3</sup>, so t³ = 2 and x = 2 + t + t², i.e. x−2 = t+t². Note 1+t+t² = (x−2)+1 = x−1. (x−2)³ = (t+t²)³ = t³(1+t)³ = 2(1+t)³. Expand (1+t)³ = 1+3t+3t²+t³ = 1+3t+3t²+2 = 3(1+t+t²) = 3(x−1). So (x−2)³ = 6(x−1). Expanding the left side: x³−6x²+12x−8 = 6x−6. Therefore x³−6x²+6x = 6x−6−12x+8+6x = 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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