#### Math - 2018-19

# AII.2 - Complex Numbers

AII.2The student willperformoperations on complex numbers andexpressthe results in simplest form using patterns of the powers of i.

*Adopted: 2016*

### BIG IDEAS

- I can express the
laws of electricity and work as an electrical engineer to design electromagnetic
fields and electronic circuits.

- I will be
able to solve quadratic equations, use the quadratic formula for all cases even
when the discriminant is a negative number, and simplify even roots of negative
numbers.

### UNDERSTANDING THE STANDARD

· A complex number multiplied by its conjugate is a real number.

· Equations having no real number solutions may have solutions in the set of complex numbers.

· Algebraic properties apply to complex numbers as well as real numbers.

· All complex numbers can be written in the form*a*+

*bi*where

*a*and

*b*are real numbers and

*i*is the imaginary unit that satisfies the equation (e.g.,

### ESSENTIALS

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

·
AII.2_{1} **Recognize**
that the square root of –1 is represented as *i*.

·
AII.2_{3} **Simplify**
powers of *i*.

·
AII.2_{2} **Simplify**
radical expressions containing negative rational numbers and **express** in *a *+ *bi* form

·
AII.2_{4} **Add**,
**subtract**, and **multiply** complex numbers.

### KEY VOCABULARY

complex
numbers, powers, *i*, field properties,
square root, simplify, radical expressions, a + b*i*, hierarchy of subsets, complex, pure imaginary, real, rational, irrational, integers, whole,
and natural numbers

*Updated: Aug 23, 2018*