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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If D < 0, the roots are:

Answer: Not real (imaginary).

  • A Real and distinct
  • B Real and equal
  • C Not real (imaginary)
  • D Rational

Correct answer: C. Not real (imaginary)

Explanation: When D < 0, sqrt(D) is imaginary. The roots are complex conjugates (not real).

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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