Answer: 0.
- A 1
- B 2
- C 3
- D 0
Correct answer: D. 0
Explanation: Sum of roots = 4, product = k²−4. Positive integer pairs summing to 4: (1,3) with product 3, or (2,2) with product 4. For product = 3: k²−4 = 3 → k² = 7 (not a perfect square, so k is irrational). For product = 4: k²−4 = 4 → k² = 8 (also irrational). Neither pair gives an integer k. So there are 0 integral values of k.
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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