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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If x² + x + 1 = 0 and roots are omega and omega², then omega<sup>100</sup> + omega<sup>200</sup> =

Answer: -1.

  • A -1
  • B 0
  • C 1
  • D 2

Correct answer: A. -1

Explanation: omega<sup>3</sup> = 1. 100 = 33×3 + 1, omega<sup>100</sup> = omega. 200 = 66×3 + 2, omega<sup>200</sup> = omega². omega + omega² = -1 (sum of cube roots of unity).

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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