New Jersey: The Complex Number System Math Standards
9 standards · 3 domains
PERFORM ARITHMETIC OPERATIONS WITH COMPLEX NUMBERS.
- N-CN.A.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.A.2 Use the relation i^2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- N-CN.A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
REPRESENT COMPLEX NUMBERS AND THEIR OPERATIONS ON THE COMPLEX PLANE.
- 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.
- 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°.
- N-CN.B.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.
USE COMPLEX NUMBERS IN POLYNOMIAL IDENTITIES AND EQUATIONS.
- N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
- N-CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).
- N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.