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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If the difference of roots of x² + bx + c = 0 is 1, then b² =

Answer: 4c+1.

  • A 4c
  • B 4c+1
  • C 4c-1
  • D c+4

Correct answer: B. 4c+1

Explanation: alpha - beta = 1. (alpha-beta)² = (alpha+beta)² - 4 alpha×beta = b² - 4c = 1. So b² = 4c + 1.

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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