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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The roots of x² - 1 = 0 are:

Answer: 1 and -1.

  • A 0 and 1
  • B 1 and -1
  • C ±√2
  • D None

Correct answer: B. 1 and -1

Explanation: x² = 1 gives x = 1 or x = -1. These are also the factor (x-1)(x+1) = 0.

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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