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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The locus of |z - 1| = 2 in the Argand plane is:

Answer: A circle of radius 2 centred at (1,0).

  • A A circle of radius 1 centred at (2,0)
  • B A circle of radius 2 centred at (1,0)
  • C A line
  • D A parabola

Correct answer: B. A circle of radius 2 centred at (1,0)

Explanation: |z - 1| = 2 represents a circle with centre at z = 1 (i.e., point (1,0)) and radius 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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