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1 Warm-up Divide the following using Long Division: (6x 3 - 16x 2 + 17x - 6) (3x –2 ) Divide the following with Synthetic Division (5x 3 – 6x 2 + 8) (x.

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Presentation on theme: "1 Warm-up Divide the following using Long Division: (6x 3 - 16x 2 + 17x - 6) (3x –2 ) Divide the following with Synthetic Division (5x 3 – 6x 2 + 8) (x."— Presentation transcript:

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

2 2 Warm-up Divide the following using Long Division: (6x x x - 6) (3x –2 ) 2x 2 – 4x + 3

3 3 Warm-up Divide the following with Synthetic Division (5x 3 – 6x 2 + 8) (x – 4)

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

5 Complex Numbers Section 2-4 Digital Lesson

6 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 7 Applications Impedance readings for electronics and electrical circuits are all measured in complex units

8 8 Complex Numbers Real NumbersImaginary Numbers RationalIrrational

9 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 10 The Imaginary Unit

11 11 Negative Radicals

12 12 Negative Radicals

13 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

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

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

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

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

18 18

19 19 Homework WS 3-7


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