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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Solve by completing the square: x² + 6x + 5 = 0

Answer: -1 and -5.

  • A -1 and -5
  • B -2 and -4
  • C 1 and 5
  • D 2 and 4

Correct answer: A. -1 and -5

Explanation: x² + 6x + 9 = 4, (x+3)² = 4, x+3 = ±2, x = -1 or x = -5.

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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