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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The locus of Im(z) = 3 in the Argand plane is:

Answer: y = 3.

  • A x = 3
  • B y = 3
  • C x² + y² = 9
  • D y = 3x

Correct answer: B. y = 3

Explanation: Im(z) = b = 3 means the imaginary part is 3. This is the horizontal line y = 3.

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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