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

Domain - The Complex Number System

Cluster - Use complex numbers in polynomial identities and equations.

[MIII.N-CN.C.8] - (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).

Resources:


  • Complex number
    A number that can be written as the sum or difference of a real number and an imaginary number.
  • Polynomial
    The sum or difference of terms which have variables raised to positive integer powers and which have coefficients that may be real or complex. The following are all polynomials: 5x3 – 2x2 + x – 13, x2y3 + xy, and (1 + i)a2 + ib2.

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.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2) – 3).
  • PC.N-CN.B.4
    (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
  • PC.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • PC.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.