Topic: The Complex Number System |
Common Core Mathematics 9-12 |
| Cluster Perform arithmetic operations with complex numbers. |
| | Grade 9-12 |
| | | N.CN.1. | 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. |
| | | N.CN.2. | Use the relation i^{2} = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. |
| | | N.CN.3. | (+) Find the conjugate of a complex number; use conjugates to find
moduli and quotients of complex numbers. |
| Cluster Represent complex numbers and their operations on the complex
plane. |
| | Grade 9-12 |
| | | N.CN.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. |
| | | N.CN.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°. |
| | | N.CN.6. | (+) 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. |
| Cluster Use complex numbers in polynomial identities and equations. |
| | Grade 9-12 |
| | | N.CN.7. | Solve quadratic equations with real coefficients that have complex
solutions. |
| | | N.CN.8. | (+) Extend polynomial identities to the complex numbers. For example,
rewrite x^{2} + 4 as (x + 2i)(x − 2i). |
| | | N.CN.9. | (+) Know the Fundamental Theorem of Algebra; show that it is true for
quadratic polynomials. |