1. 5-6: Complex Numbers Day 1 (Essential Skill Review)
Essential Question: How do we simplify square roots of negative numbers?

2. 5-6: Complex Numbers Operations with Radicals
Simplifying a radical: Option #1
Break a number into prime factors.
Pull any pairs out as one number outside the radical
Multiply any numbers remaining inside & outside the radical
Example #1
75 = 5 • 5 • 3 =
Example #2
96 = 2 • 2 • 2 • 2 • 2 • 3 = 2 • 2

3. 5-6: Complex Numbers Operations with Radicals
Simplifying a radical: Option #2
Divide by perfect squares.
A perfect square is any number times itself:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, etc.
Simplify all portions of the radical
Example #1
Example #2

4. 5-6: Complex Numbers Some rules with radicals
When numbers INSIDE a radical match, the numbers OUSTIDE can be added/subtracted (rule of like terms)
Sometimes, radicals must be simplified before they can be combined
Example:

5. 5-6: Complex Numbers Some rules with radicals (continued)
You shouldn’t leave a radical in the denominator of a fraction
To remove it, we rationalize the denominator. Multiply the top and bottom of the fraction by the radical in the denominator.
Examples:

6. 5-6: Complex Numbers
Assignment
Page 883
2 – 30, evens

7. 5-6: Complex Numbers Day 2
Essential Question: How do we simplify square roots of negative numbers?

8. 5-6: Complex Numbers
The imaginary number i is defined as the number whose square is -1.
So i2 = -1, and
To simplify square roots of negative numbers
Take the negative sign outside the square root, replace it with i.
Simplify the number underneath the square root as normal. Numbers outside the square root come before the i.
Example:

9. 5-6: Complex Numbers
Solve

10. 5-6: Complex Numbers
Imaginary numbers and real numbers make up the set of complex numbers.
Complex numbers are written in the form a + bi
That means the real number gets written first, followed by the imaginary number.
Example:
Write the complex number in the form a + bi

11. 5-6: Complex Numbers
Write the complex number in a + bi form.

12. 5-6: Complex Numbers
You can apply real number concepts to complex numbers.
Complex numbers have additive inverses (or “opposites”)
It’s simply the opposite of the real number added to the opposite of the imaginary number
Example: Find the additive inverse of i.
The opposite of -2 is 2
The opposite of 5i is -5i.
So the additive inverse of i is 2 – 5i.

13. 5-6: Complex Numbers
Find the additive inverse of each number

14. 5-6: Complex Numbers Assignment Page 274 Problems 1 – 18 and 24 – 28
All problems

15. 5-6: Complex Numbers Day 3
Essential Question: How do we simplify square roots of negative numbers?

16. 5-6: Complex Numbers Adding & Subtracting Complex Numbers Example
Simply combine the real parts with the imaginary parts
Example
(5 + 7i) + (-2 + 6i)
i + 6i
3 + 13i

17. 5-6: Complex Numbers
Simplify each expression

18. 5-6: Complex Numbers Multiplying Complex Numbers Example
If i = , then i2 = -1
Example
(5i)(-4i)
-20i2
Replace i2 with -1
-20(-1) 20

19. 5-6: Complex Numbers
Simplify the expression

20. 5-6: Complex Numbers Multiplying Complex Numbers FOIL Example
(2 + 3i)(-3 + 5i)
i – 9i + 15i2 Combine like terms
-6 + i + 15(-1) Replace i2 with -1
-6 + i – 15 Combine like terms again
-21 + i

21. 5-6: Complex Numbers
Simplify the expression

22. 5-6: Complex Numbers
Simplify the expression

23. 5-6: Complex Numbers Assignment Page 274
Problems (all) and (even)