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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The locus of z for which arg((z − 1)/(z + 1)) = π/2 is:

Answer: An arc of the circle x² + y² = 1.

  • A The line x = 0
  • B An arc of the circle x² + y² = 1
  • C A parabola
  • D The entire real axis

Correct answer: B. An arc of the circle x² + y² = 1

Explanation: The segment joining −1 and 1 subtends a right angle at z, so z lies on the circle with that segment as diameter, x² + y² = 1 (the arc where the angle is +π/2).

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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