Standards Map

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 - Represent complex numbers and their operations on the complex plane.

[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.

Resources:


  • Complex number
    A number that can be written as the sum or difference of a real number and an imaginary number.
  • Complex plane
    The coordinate plane used to graph complex numbers.
  • Imaginary number
    Complex numbers with no real terms, such as 5i.
  • Polar form
    The polar coordinates of a complex number on the complex plane. The polar form of a complex number is written in any of the following forms: rcos θ + r i sinθ , r(cos θ + i sinθ), or r cis θ. In any of these forms, r is called the modulus or absolute value. θ is called the argument.
  • 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:

  • AII.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 x-a and b real.
  • AII.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • 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.
  • MIII.N-CN.C.8
    (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
  • PC.N-CN.A.3
    (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
  • PC.N-CN.B.5
    (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example: (-1+√3i)3=8 because (-1+ √3i) has modulus 2 and argument 120°.