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Mathematics > Course Model Mathematics II (Integrated Pathway) > The Complex Number System
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - The Complex Number System

Cluster - Use complex numbers in polynomial identities and equations.

[MII.N-CN.C.7] - Solve quadratic equations with real coefficients that have complex solutions.

Resources:


  • Coefficient
    Any of the factors of a product considered in relation to a specific factor.
  • Complex number
    A number that can be written as the sum or difference of a real number and an imaginary number.
  • Quadratic equation
    An equation that includes only second degree polynomials. Some examples are y = 3x2 – 5x2 + 1, x2 + 5xy + y2 = 1, and 1.6a2 +5.9a – 3.14 = 0.
  • Real number
    A number from the set of numbers consisting of all rational and all irrational numbers.

Predecessor Standards:

No Predecessor Standards found.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.N-CN.A.1
    Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.
  • MII.N-CN.A.2
    Use the relation i2 = –1 and the Commutative, Associative, and Distributive properties to add, subtract, and multiply complex numbers.
  • 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.
  • PC.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.