Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.
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Transcript of Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.
![Page 1: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/1.jpg)
Homework
WB p.3-4 #36-54 (evens or odds)
![Page 2: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/2.jpg)
Chapter 1 Review
![Page 3: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/3.jpg)
The Complex Numbers
Real numbers:
Imaginary numbers:
Pure imaginary numbers:
is the imaginary unit
Who remembers what equals? Think about this: What makes an imaginary number “imaginary”?
What about ? Let’s keep going! Notice a pattern?
All radical properties are the same in the imaginary world!
![Page 4: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/4.jpg)
Radicals & Imaginary Numbers
Example #1:
Example #2:
![Page 5: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/5.jpg)
Adding and Subtracting Complex Numbers
Example #1:
Example #2:
![Page 6: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/6.jpg)
More conjugates!
How do we find the complex conjugate of the following?
![Page 7: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/7.jpg)
Same rules as radicals- we never, ever, ever leave an imaginary numbers in the denominator! Multiply by the conjugate or !
Simplify the following:
![Page 8: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/8.jpg)
Quadratic Functions
How many solutions do quadratics have (always!)?
How do we solve quadratics?
4 ways:
-Quadratic Formula
-Factoring
-Completing the Square
-Graphing (not often)
***GOLDEN RULE OF SOLVING QUADRATICS: There must be a 0 on one side of the equation!!
![Page 9: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/9.jpg)
Who remembers the quadratic formula?!
Let’s solve this using the quadratic formula- just substitute your values for a, b, and c!
![Page 10: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/10.jpg)
Another one- this one may be more “complex”
![Page 11: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/11.jpg)
Factoring
This is the opposite of distributing.
***Make sure you first factor out the common factors!
Ex)
![Page 12: Homework WB p.3-4 #36-54 (evens or odds). Chapter 1 Review.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697c00f1a28abf838cca683/html5/thumbnails/12.jpg)
Another one- factor this!