1. 5.4 Complex Numbers

2. Square Roots
Square root: For any real numbers a and b, if a2 = b, then a is a square root of b.

3. Examples
Simplify
Answers

4. Complex Numbers Imaginary number (unit): denoted by i
Pure Imaginary Numbers: 3i, -5i, i√2
Ex.1
Ex.2 a) b)

5. Multiplying Imaginary #’s
Ex.3
Ex.4
**Change to Imaginary numbers 1st
Ex.5
Try this one

6. Powers of i

7. Powers of i
Simplify Ex. 6
Try this one Ex. 7

8. Equations with Imaginary Solutions
Solve the following equation Ex. 8
**Must include + when √ both sides.

9. Complex Numbers Complex Numbers
a + bi (a & b are real #’s) – Standard Form
a is the real part, b is the imaginary part
Find x and y that make the equation true
Ex.9 a b a b

10. Example Problems Ex. 10 (2 – 5i) – (8 + 6i) FOIL
Distribute the negative and combine like terms
Ex (2 – 5i) – (8 + 6i)
-6 – 11i
FOIL
Ex (3 – 4i)(2 + i)
10 – 5i

11. Complex Conjugates Two complex numbers of the form a + bi and a – bi
Example: 3 – 4i conjugate = 3 + 4i
Example: i conjugate = 2 – 3i
Ex.12
**Put your answer in the standard form (a + bi).

12. Homework Assignment #25
p odd, 78, 79