1. Warm-up Divide the following using Long Division:
(6x3 - 16x2 + 17x - 6)  (3x –2 )
Divide the following with Synthetic Division
(5x3 – 6x2 + 8) (x – 4)
Given the following polynomial and one of its factors, Find the remaining factors
(3x3 + 2x2 –19x + 6) : (x + 3) is a factor

2. Warm-up Divide the following using Long Division:
(6x3 - 16x2 + 17x - 6)  (3x –2 )
2x2 – 4x + 3

3. Warm-up Divide the following with Synthetic Division
(5x3 – 6x2 + 8) (x – 4)

4. Warm-up
Given the following polynomial and one of its factors, Find the remaining factors
(3x3 + 2x2 –19x + 6) : (x + 3) is a factor
(x – 2)(3x – 1)

5. Complex Numbers Section 2-4
Digital Lesson
Complex Numbers Section 2-4

6. Objectives I can use “i” to write complex numbers
I can add, subtract, and multiply complex numbers
I can simplify Negative Square Roots

7. Applications
Impedance readings for electronics and electrical circuits are all measured in complex units

8. Complex Numbers
Real Numbers Imaginary Numbers
Rational Irrational

9. Complex Numbers
The set of all numbers that can be written in the format: a + bi ;
“a” is the real number part
“bi’ is the imaginary part

10. The Imaginary Unit

11. Negative Radicals

12. Negative Radicals

13. Add or Subtract Complex Numbers
To add or subtract complex numbers:
1. Write each complex number in the form a + bi.
2. Add or subtract the real parts of the complex numbers.
3. Add or subtract the imaginary parts of the complex numbers.
(a + bi ) + (c + di ) = (a + c) + (b + d )i
(a + bi ) – (c + di ) = (a – c) + (b – d )i
Add or Subtract Complex Numbers

14. Adding Complex Numbers
Example: Add (11 + 5i) + (8 – 2i )
= (11 + 8) + (5i – 2i )
Group real and imaginary terms.
= i
a + bi form
Adding Complex Numbers

15. Subtracting Complex Numbers
Examples: Subtract: (– i ) – (7 – 9i)
= (– 21 – 7) + [(3 – (– 9)]i
Group real and imaginary terms.
= (– 21 – 7) + (3i + 9i)
= – i
a + bi form
Subtracting Complex Numbers

16. Product of Complex Numbers
The product of two complex numbers is defined as:
(a + bi)(c + di ) = (ac – bd ) + (ad + bc)i
1. Use the FOIL method to find the product.
2. Replace i2 by – 1.
3. Write the answer in the form a + bi.
Product of Complex Numbers

17. 1. 7i (11– 5i) = 77i – 35i2
= 77i – 35 (– 1)
= i
2. (2 + 3i)(6 – 7i ) = 12 – 14i + 18i – 21i2
= i – 21i2
= i – 21(–1)
= i + 21
= i
Examples

19. Homework
WS 3-7