Code | Grade | Cluster | Standard | Object Count |

N-CN.1 |
High School - Number and Quantity |
Perform arithmetic operations with complex numbers. |
Know there is a complex number i such that i^2 = –1, and every complex number has the form a + bi with a and b real. |
0 |

N-CN.2 |
High School - Number and Quantity |
Perform arithmetic operations with complex numbers. |
Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. |
1 |

N-CN.3 |
High School - Number and Quantity |
Perform arithmetic operations with complex numbers. |
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. |
0 |

N-CN.4 |
High School - Number and Quantity |
Represent complex numbers and their operations on the complex plane. |
(+) 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. |
0 |

N-CN.5 |
High School - Number and Quantity |
Represent complex numbers and their operations on the complex plane. |
(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + v3 i)^3 = 8 because (-1 + v3 i) has modulus 2 and argument 120°. |
0 |

N-CN.6 |
High School - Number and Quantity |
Represent complex numbers and their operations on the complex plane. |
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. |
0 |

N-CN.7 |
High School - Number and Quantity |
Use complex numbers in polynomial identities and equations. |
Solve quadratic equations with real coefficients that have complex solutions. |
1 |

N-CN.8 |
High School - Number and Quantity |
Use complex numbers in polynomial identities and equations. |
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i). |
0 |

N-CN.9 |
High School - Number and Quantity |
Use complex numbers in polynomial identities and equations. |
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
1 |