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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If z = a + ib, then z × z-bar (conjugate) =

Answer: a² + b².

  • A a² - b²
  • B 2ab
  • C a² + b²
  • D a + b

Correct answer: C. a² + b²

Explanation: z x z-bar = (a+ib)(a-ib) = a<sup>2</sup>+b<sup>2</sup> = |z|<sup>2.</sup>

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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