## 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.

### Use the relation i^{2} = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

## 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 + √3 i)^{3} = 8 because (-1 + √3 i) has modulus 2 and argument 120°.

## Use complex numbers in polynomial identities and equations.

### Solve quadratic equations with real coefficients that have complex solutions.

### (+) Extend polynomial identities to the complex numbers. For example, rewrite x^{2} + 4 as (x + 2i)(x – 2i).

### (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

Common Core Math

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### Eighth Grade

### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School