MAT1275 College Algebra and Trigonometry, FA2018

Topics:

• Definition of a complex number

• Real and Imaginary parts of a complex number

• Complex conjugates

• Product of complex conjugates: Theorem: $(a+bi)(a-bi) = a^{2}+b^{2}$ (easy to prove).

• Division of complex numbers (rationalizing the denominator really)

• New topic: quadratic equations and the Zero Product Property

Zero Product Property: If AB = 0, then either A=0 or B=0.

Homework:

• Make sure that you have activated your Piazza account! If you are not sure how to do this, email me!

• This would also be a good moment to review my course policies and WeBWorK policies.

• Review the material and examples we discussed in class. You may also need to review factoring polynomials and the ac method: I will post some more links on this blog when I have a chance.

• Do the WeBWorK  assignments, due by Sunday midnight, but don’t wait to the last minute!

• Also do and check (per my Course Policies) the following problems from the textbook. You may put one of these on the board at or before the start of class (Just do it, don’t wait, but also don’t duplicate another student’s problem) as part of your 10 problems:

Complex Numbers: p. 559 #77-89 odd

Also do the following that I put on the board in class:

Check the solution $x = -\frac{5}{6}$ in the equation $9x(4x+2) – 10x = 8x + 25$

Solve the equation $5a(2a-3) +4(a+1) = 3a(3a-2)$ using the Zero Product Property

Remember that if you get stuck on any of the problems or have a question about any of the material, you can post a question to the Piazza discussion board.

Here are solutions to Test 1, depending on which version you got:

MA1275Test1AanswersFall2018

MA1275Test1BanswersFall2018

(after Test 1)

TO BE UPDATED!!!

Topic: Complex Numbers and powers of i

sources:

Cool Math: What are complex numbers?

On powers of i

Test 1 is rescheduled for Monday 15 October.

Test 1 is scheduled for the first 50 minutes or so of class on Monday 15 October (CORRECTION!!!). Please see my course information for policies related to tests.
Here are two self-tests showing the material that will be covered on Test 1. Use them to test yourself.

MAT1275Test1ReviewFall2018

Here are the answers: please note that the work has not been shown in these, but you will be graded on your work! Therefore, make sure that you also check the sections/examples listed below to make sure that you are using correct methods for the problems. It can also be useful to look at old WeBWorK problems, which often have detailed solutions and explanations available!

In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.

MAT1275Test1ReviewAnswersFall2018

Please make use of the Piazza discussion board if you find any typos in these or if you want to discuss.

Review sections/examples for each problem:

Self-Test A

1) See Section  4.1 Examples 1-6 and MAT1275ExponentsDefinitionsLaws

2) See Section 5.4 Complex Fractions  Examples 1-2 (Method I) Examples 3-5 (Method II)

3) See Section 5.4 Complex Fractions  Examples 1-2 (Method I) Examples 3-5 (Method II)

4) See Section 5.3

5) See Section 5.3

6) See Section 5.5

7) See Section 5.5

8) See Section 6.1

9) See Section 6.3

10) See Sections 6.1, 6.3

Self-Test B

The sections/examples are on the answer sheet.

Due to unforeseen complications, the posts for yesterday’s class and for the Test 1 review are delayed. I expect to be able to post them this evening sometime. In the meantime, make sure that you check last time’s post and also look at the new WeBWorK assignment.

Topics:

In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.

• Simplifying Radical Expressions

• Addition and Subtraction of Radicals

Homework:

• Study the examples discussed in class: make sure that you understand the notation and vocabulary that is being used.

• Make sure that you have signed into WeBWorK (and do the assignments) and that you have joined the Piazza discussion group. I am directing Piazza to re-send the invitation to those students who have not yet activated their Piazza accounts.

• You may join OpenLab and join this course on OpenLab if you wish. It is not required: you can read this blog without joining. But membership has its benefits!

• Make sure to check this OpenLab site for homework which is being set up to post automatically after every class from now on, and I may even post notes for upcoming classes so you could print them out and bring to class!

Topics:

In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.

• Roots and Radicals – there are two WeBWorK assignments on this topic, named  “Higher Roots” and “Higher Roots Algebraic”

• Rational Exponents

Here are a complete set of notes on exponents and their properties, which contain everything we have discussed so far and also notes on the definition of fractional (rational) exponents:
MAT1275ExponentsDefinitionsLaws

Homework:

• Study the examples discussed in class: make sure that you understand the notation and vocabulary that is being used.

• Make sure that you have signed into WeBWorK (and do the assignments) and that you have joined the Piazza discussion group. I am directing Piazza to re-send the invitation to those students who have not yet activated their Piazza accounts.

• You may join OpenLab and join this course on OpenLab if you wish. It is not required: you can read this blog without joining. But membership has its benefits!

• Make sure to check this OpenLab site for homework which is being set up to post automatically after every class from now on, and I may even post notes for upcoming classes so you could print them out and bring to class!

Topics:

In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.

• Complex Fractions Method II

In this method, we simplify a complex fraction as follows:

First find the LCM of all the denominators in the top and bottom of the complex fraction

Then multiply the top and bottom of the complex fraction by the LCM – don’t forget to distribute!

Then cancel: each denominator in the top and bottom should now be eliminated. We call this “clearing the denominators”.

Then simplify more if necessary.

Make sure that you understand and can use both methods! Sometimes one is easier than the other, and you will learn how to know this by experience. It’s a good idea to use both methods in the beginning until you see how they work.

Here are some outline notes (you can fill in the computations) on both methods for simplifying complex fractions:

MAT1275ComplexFractions

• Solving Fractional Equations (Rational Equations)

We solve these equations by using the LCM of all the denominators to clear the denominators by multiplying both sides by the LCM (and don’t forget to distribute!). You do not need to change to a common denominator, and you should not do so – it only makes solving harder.

Also, beware that sometimes you get “solutions” from this method which are not solutions of the original equation, because they lead to a 0 denominator when you substitute back in. Therefore it is necessary to check all solutions to see of they really are solutions, when solving a rational equation!

Topics:

In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.

Those videos were especially selected by teachers of MAT 1275 here at City Tech, so you know they can be trusted!

• Finding LCMs by factoring denominators – Note that I will always refer to these as the LCM (lowest common multiple) rather than the LCD (lowest common denominator), because we do not always use them as a denominator. For example, in the second method of simplifying complex fractions, we will use the LCM to get rid of denominators, and we do this also in solving equations that have rational expressions in them. See this post.

• Addition and subtraction of rational expressions.

To add or subtract rational expressions, they must have the same denominators. If necessary, we change to a common denominator (the LCM of the denominators).

• Complex Fractions Method I

In this method, we simplify a complex fraction as follows:

First simplify the numerator and the denominator separately (if necessary)

Then turn the division into multiplying by the reciprocal of the denominator.

Note: method II next time.