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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If |x - 1| + |x + 1| = 2, then x belongs to:

Answer: [-1, 1].

  • A x = 0 only
  • B [-1, 1]
  • C {-1, 1}
  • D All real x

Correct answer: B. [-1, 1]

Explanation: Case analysis on |x|: Case 1: x < -1: (1-x)+(-x-1)=-2x=2, x=-1 (boundary). Case 2: -1≤x≤1: (1-x)+(x+1)=2=2, always true. Case 3: x>1: (x-1)+(x+1)=2x=2, x=1 (boundary). So the full solution set is [-1,1]. Answer: x ∈ [-1, 1]

Argand Plane: z = a + ibReImz = a+iba (real part)b (imaginary part)θ = arg(z)|z| = length of the vector OZ = √(a²+b²); θ = angle OZ makes with the positive real axis

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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