Mathematics | Course : Model Mathematics II (Integrated Pathway)
Domain - The Complex Number System
Cluster - Perform arithmetic operations with complex numbers.
[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.
- Complex number
A number that can be written as the sum or difference of a real number and an imaginary number. - Real number
A number from the set of numbers consisting of all rational and all irrational numbers.
[MII.N-RN.B.3] -
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
[MII.N-CN.A.2] -
Use the relation i2 = –1 and the Commutative, Associative, and Distributive properties to add, subtract, and multiply complex numbers.
[MII.N-CN.C.7] -
Solve quadratic equations with real coefficients that have complex solutions.
[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.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).