5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number?...
-
Upload
patrick-carpenter -
Category
Documents
-
view
223 -
download
0
description
Transcript of 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number?...
![Page 1: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/1.jpg)
5.4 Complex Numbers
p. 272What is an imaginary number?How is it defined?What is a complex number? How is it graphed?How do you add, subtract, multiply and divide complex
numbers?What is a complex conjugate? When do you use it?How do you find the absolute value of a complex
number?
![Page 2: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/2.jpg)
Algebra 2C--Section 5.4•She used her imagination to write the story.•His imagination helped him with the role in the play.•He was able to draw the picture of the house he wanted to build using his imagination.•She had a tea party with her imaginary friends.•Define imagination.•Define imaginary.•What is the difference?
![Page 3: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/3.jpg)
Solve:
x2 = 1
x2 = -1
![Page 4: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/4.jpg)
Define the word: complex
• He gave a complex explanation.• It was a complex math problem.• He turned a simple solution into a complex solution.
![Page 5: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/5.jpg)
Imaginary Unit Definition
i = √−1 and i 2 = −1
![Page 6: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/6.jpg)
Complex number
A complex number is made up of a real number and an imaginary number.
Standard form for a complex number is: a + bi
a is the real part and bi is the imaginary part.If a = 0 and b ≠ 0, then a + bi is a pure
imaginary number (0 + bi).
![Page 7: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/7.jpg)
Plotting Complex Numbersa)2 – 3i b) -3 + 2i c) 4i
![Page 8: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/8.jpg)
Adding and Subtracting Complex Numbers
(4 – i) + (3 + 2i)
(7 – 5i) – (1 – 5i)
6 – (−2 + 9i) + (−8 + 4i)
![Page 9: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/9.jpg)
Multiplying Complex Numbers
5i(−2 + i)
(7 – 4i)(−1 + 2i)
(6 + 3i)(6 – 3i)
![Page 10: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/10.jpg)
Complex Conjugates
The two factors of the last problem were6 + 3i and 6 – 3i. They have the form of a + bi and a – bi. They are like (a+b)(a−b)
that have a middle term of 0 when multiplied together.
The product of a complex conjugate is always a real number.
![Page 11: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/11.jpg)
Dividing Complex Numbers
Write the quotient in standard form.
5 + 3i1− 2i
![Page 12: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/12.jpg)
Finding Absolute Values of Complex Numbers
a) 3 + 4i1. Use the numbers in the
complex number 3 + 42. Square the numbers 32 + 42
3. Take the square root √32 + 42
![Page 13: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/13.jpg)
Finding Absolute Values of Complex Numbers
b.-2i
c. -1 +5i
![Page 14: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/14.jpg)
What is an imaginary number?How is it defined?What is a complex number? How is it graphed?How do you add, subtract, multiply and divide
complex numbers?What is a complex conjugate? When do you use
it?How do you find the absolute value of a complex
number?
![Page 15: 5.4 Complex Numbers p. 272 What is an imaginary number? How is it defined? What is a complex number? How is it graphed? How do you add, subtract, multiply.](https://reader036.fdocuments.in/reader036/viewer/2022082412/5a4d1b077f8b9ab059988d2d/html5/thumbnails/15.jpg)
Assignment 5.4
Page p. 277, 17-69 odd