1. Complex Numbers and Solving Equations
Honors Algebra II with Trig.
Mr. Agnew

2. Essential Stuff Essential Question Essential Vocabulary
How do you simplify expressions involving complex numbers?
Essential Vocabulary
Imaginary Number
Complex Number
Complex Conjugate

3. Imaginary Numbers
Not all quadratic equations have real number solutions, so to overcome this problem, mathematicians created an expanded system of numbers using the imaginary unit 𝐢

4. Imaginary Unit, 𝒊
𝒊= −𝟏 𝒊 𝟐 =−𝟏
These properties allow us to simply the square root of a negative number.

5. Complex Numbers
A complex number is a number that contains a real and an imaginary part.
The standard form: 𝒂+𝒃𝒊
Real
Imaginary

6. Add/Subtract/Multiply
Add and Subtract
Combine Like Terms
Write in Standard Form
Multiply
FOIL
Replace 𝒊 𝟐 with −𝟏
Combine Like Terms/Standard Form

7. Dividing with Complex Numbers
Divide
Multiply the numerator and denominator by the complex conjugate
Complex conjugates are two complex numbers of the form:
𝒂+𝒃𝒊 and 𝒂−𝒃𝒊

8. The product of complex conjugates will always be a real number.

9. Homework
Homework 5.5: Complex Numbers