MATH Basic Algebra II  - Unit 14: Complex Numbers
The Discriminant

For the first three problems, find the discriminant, and determine the number of solutions and type of solutions for each quadratic:  2 real, 2 imaginary, or 1 real.

Click here to view a chart about the types of solutions of a quadratic equation in a pop-up window.

1) What is the discriminant?  How many and what type of solutions does the quadratic have?

20000 character(s) left



Attachments
There are no attachments
 Attach a File
2) What is the discriminant?  How many and what type of solutions does the quadratic have?

4000 character(s) left

3) What is the discriminant?  How many and what type of solutions does the quadratic have?

4000 character(s) left

Imaginary Numbers

 

4) Simplify.
 
Hint:  Begin by factoring (–1)(169).

5) Simplify.

6) Simplify.

In the following problems use the cyclic nature of the powers of "i" and the pattern that repeats every 4 numbers to determine the value.

7) Evaluate.

8) Evaluate.

Complex Numbers

In the following problems, use the quadratic formula to solve.

9) Solve for x.

10) Solve for x.
 
Hint:  Put the quadratic equation in standard form so that only a zero is on the right side.

11) Solve for x.

12) Solve for x.

Computing with Complex Numbers

For the following problems, add or subtract.

13) What is the sum?

14) What is the difference?
 
Hint:  When subtracting a quantity, use addition AFTER changing the signs of the terms inside parenthesis to their opposites.

15) What is the difference?

In the following problems, multiply using the FOIL method.

 

16) What is the product?

17) What is the product?

18) What is the product?

19) What is the product?

Conjugate of a Complex Number
 

 

Complex number conjugates (CC)

 

In the following problems, rationalize the denominator for the given complex number.

20) Simply the given complex number by rationalizing the denominator.
 
Hint:  To simplify, multiply both the numerator and the denominator by the conjugate of the denominator.

21) Simply the given complex number by rationalizing the denominator.

22) Simply the given complex number by rationalizing the denominator.

Review

23) Find the slope of a line containing the points (2, 3) and (–6, –4).
 
Click here to review the unit content explanation for Linear Equations.

250 character(s) left

24) Solve for x: 2x + 3(x – 2) = –3
 
Click here to review the unit content explanation for Solving Equations and Applications.

250 character(s) left

25) Solve the inequality for x.
 
Click here to review the unit content explanation for Inequalities and Absolute Value Equations.

250 character(s) left

26) Solve the absolute value equation for x.
 
Hint:  Recall that absolute value equations may have two solutions, one solution, many solutions, or no solution.  This particular absolute value equation has two solutions.
 
Click here to review the unit content explanation for Inequalities and Absolute Value Equations.

250 character(s) left

27) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.
No offline activities found
0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.



Attachments
There are no attachments
 Attach a File