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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The equation x² - 2ax + a² - 1 = 0 has roots in (-2, 4). Range of a:

Answer: -1 < a < 3.

  • A -1 < a < 3
  • B 1 < a < 3
  • C -1 < a < 5
  • D 0 < a < 4

Correct answer: A. -1 < a < 3

Explanation: Factor: (x-a)²=1, so roots are x=a+1 and x=a-1. Both must lie in (-2,4): a-1 > -2 gives a > -1; a+1 < 4 gives a < 3. Combining both conditions: -1 < a < 3. Answer: -1 < a < 3

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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