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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Which of these quadratic expressions is always positive?

Answer: x² - x + 1.

  • A x² - x + 1
  • B x² - 4
  • C x² - 2x
  • D x² - 3x - 4

Correct answer: A. x² - x + 1

Explanation: D = 1 - 4 = -3 < 0 and a > 0 for x² - x + 1. Negative D + positive a means always positive.

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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