Answer: Both A and B.
- A (p²-2q)² - 2q²
- B p<sup>4</sup> - 4p²q + 2q²
- C (p²-q)² - q²
- D Both A and B
Correct answer: D. Both A and B
Explanation: alpha²+beta² = p²-2q. alpha<sup>4</sup>+beta<sup>4</sup> = (alpha²+beta²)² - 2(alpha×beta)² = (p²-2q)² - 2q². Expanding: p<sup>4</sup>-4p²q+4q²-2q² = p<sup>4</sup>-4p²q+2q². Both expressions are equal.
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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