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Mathematics > Course Model Precalculus (Advanced Course) > The Complex Number System
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Mathematics | Course : Model Precalculus (Advanced Course)

Domain - The Complex Number System

Cluster - Use complex numbers in polynomial identities and equations.

[PC.N-CN.C.9] - (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Resources:


  • Fundamental Theorem of Algebra
    The theorem that establishes that, using complex numbers, all polynomials can be factored into a product of linear terms. A generalization of the theorem asserts that any polynomial of degree n has exactly n zeros, counting multiplicity.
  • Quadratic polynomial
    A polynomial where the highest degree of any of its terms is 2.

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the solutions of a quadratic equation results in non-real solutions and write them as a ± bi for real numbers a and b.
  • AII.N-CN.C.7
    Solve quadratic equations with real coefficients that have complex solutions.
  • AII.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • AII.A-APR.B.2
    Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
  • MII.N-CN.C.7
    Solve quadratic equations with real coefficients that have complex solutions.
  • MII.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
  • MIII.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • MIII.A-APR.B.2
    Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).