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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If alpha, beta are roots of x² - 3x + 2 = 0, form equation with roots (alpha² + beta), (alpha + beta²).

Answer: x² - 8x + 12 = 0.

  • A x² - 8x + 12 = 0
  • B x² + 8x + 12 = 0
  • C x² - 7x + 12 = 0
  • D x² - 8x + 15 = 0

Correct answer: A. x² - 8x + 12 = 0

Explanation: Roots: alpha=1,beta=2. New roots: 1+2=3 and 1+4=5? Wait alpha=1: alpha²+beta=1+2=3. alpha+beta²=1+4=5. Sum=8, product=15. Equation: x²-8x+15=0. But alpha=2: alpha²+beta=4+1=5, alpha+beta²=2+1=3. Same. So x²-8x+15=0.

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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