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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

For a quadratic with negative discriminant, the parabola:

Answer: Never crosses x-axis.

  • A Crosses x-axis twice
  • B Touches x-axis once
  • C Never crosses x-axis
  • D Is undefined

Correct answer: C. Never crosses x-axis

Explanation: D < 0: no real roots means the parabola does not intersect the x-axis at all. It is entirely above or below.

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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