AII.2 - Complex Numbers

AII.2  The student will perform operations on complex numbers and express the results in simplest form using patterns of the powers of i.

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

2016 VDOE Curriculum Framework - AII.2 Understanding

·  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.21  Recognize that the square root of –1 is represented as i.

·  AII.23  Simplify powers of i.

·  AII.22  Simplify radical expressions containing negative rational numbers and express in a + bi form

·  AII.24  Add, subtract, and multiply complex numbers.

KEY VOCABULARY

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

Updated: Aug 23, 2018