Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with...
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Transcript of Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with...
![Page 1: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/1.jpg)
Warm-up
• Solve for x. 1.
2.
3.
4. 0852
025
32954
64
2
2
2
2
xx
xx
x
x
![Page 2: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/2.jpg)
Section 5-6: Complex Numbers
Goal 1.02: Define and compute with complex numbers.
![Page 3: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/3.jpg)
Essential Questions
• What is an imaginary number?
• Why is it important to be able to compute with imaginary numbers?
![Page 4: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/4.jpg)
Imaginary Numbers
1
1
1
4
3
2
i
ii
i
i
![Page 5: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/5.jpg)
Simplifying Numbers using i:
![Page 6: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/6.jpg)
Complex Number comprised of an imaginary and a real number of the form:
Complex Number Plane:
bia
i43
![Page 7: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/7.jpg)
Absolute Value of a Complex Number:
a: |6 – 4i|
b: |-2 + 5i|
c: |5i|
22 babia
![Page 8: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/8.jpg)
Additive Inverse of a Complex Number:
bia
i
i
i
3
34
52
![Page 9: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/9.jpg)
Adding and Subtracting Complex Numbers:
ii
i
ii
ii
3)64(
)23(7
)42()38(
)62()75(
![Page 10: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/10.jpg)
Multiplying Complex Numbers:
)34)(56(
)53)(32(
)32)(32(
)3)(7(
)4)(5(
ii
ii
ii
ii
ii
![Page 11: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/11.jpg)
Dividing Complex Numbers:
iiiiii
iii
i
i
i
ii
i
5
1
5
8
5
8
41
624221
6342
21
21
21
3221
32
2
2
Multiply by the conjugate.
Multiply binomials.
Simplify.
![Page 12: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/12.jpg)
Finding Complex Solutions:
a: 3x2 + 48 = 0
b: 4x2 + 100 = 0
c: 8x2 + 2 = 0
![Page 13: Warm-up Solve for x. 1. 2. 3. 4.. Section 5-6: Complex Numbers Goal 1.02: Define and compute with complex numbers.](https://reader036.fdocuments.in/reader036/viewer/2022082821/5697c01e1a28abf838cd0faf/html5/thumbnails/13.jpg)
Classwork/ Homework
• P. 274• Classwork: #2-18 Even
• Homework: #20-46 Even