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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Solve x² + x + 1 = 0. The roots are:

Answer: Imaginary (complex).

  • A Real and distinct
  • B Equal and real
  • C Imaginary (complex)
  • D Rational

Correct answer: C. Imaginary (complex)

Explanation: D = 1 - 4 = -3 < 0. Roots are complex (imaginary).

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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