Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
Approach #1
Answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions you were unable to do, for which you got an incorrect answer, or for which you would like some further explanation.
Approach #2
Proceed directly to the first page of the lesson without attempting the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test later and use it as a worksheet.
Pre-test
For exercises 1 to 12, perform the indicated operations and express your answer in simplest terms.
1. (2 + 3i ) + (5 + 4i ) 2. (-1 - 7i ) + (-6 - 9i ) 3. 
4. 
5. 
6. 
7. (2 + 3i )(4 + 7i ) 8. 
9. 
10. 
11. 
12. 
13. Verify that -3 + 4i and -3 - 4i are roots of the equation x2 + 6x + 25 = 0.
14. Verify that 
, 
and -1 are roots of the equation 4x3 + x + 5 = 0.
15. What does exercise 13 - 14 suggest about complex roots of polynomial equations?
Students will be expected to:
- Identify, add, subtract, and multiply complex numbers.
- Verify complex numbers as solutions to polynomial equations.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- Definition of pure imaginary numbers.
- How to add, subtract and multiply complex numbers.
- The conjugate of a binomial that has a radical term.
- Concept of the roots of an equation and the zeros of a function.