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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If alpha, beta are roots of x² - px + q = 0, then alpha² + beta² =

Answer: p² - 2q.

  • A p² - q
  • B p² - 2q
  • C p² + 2q
  • D 2p - q

Correct answer: B. p² - 2q

Explanation: alpha² + beta² = (alpha+beta)² - 2 alpha×beta = p² - 2q.

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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