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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If α and β are the roots of x² − 2x + 4 = 0, then α⁶ + β⁶ equals:

Answer: 128.

  • A 64
  • B −64
  • C 128
  • D −128

Correct answer: C. 128

Explanation: The roots are 2e<sup>±iπ/3</sup>. So α⁶ + β⁶ = 2·2⁶·cos(2π) = 128.

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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