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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Solve: x² - 4 = 0

Answer: x = ±2.

  • A x = 2, just one of the two valid roots
  • B x = -2, just the other valid root alone
  • C x = ±2
  • D x = ±4, doubling the actual correct values

Correct answer: C. x = ±2

Explanation: x² = 4, so x = ±√4 = ±2. Square roots always give two values (positive and negative).

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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