Learning Resources
Lesson
During this Investigation you will learn to multiply and divide complex numbers. As well, you will learn to "realize" the denominator of fractions involving complex numbers.
Carry out the procedure as outlined on pages 283 & 284 of your text., drawing accurate graphs for each step. Hints and suggestions are provided for various steps. Be sure to view the hint for Step J as it contains a correction to an error in the text. Use the other hints only if you are experiencing difficulty.
You will need to recall how to graphically illustrate the sum of two vectors. This process was studied in Focus C in the previous lesson.
Answer the Investigation Questions.
A summary of the Investigation is provided.
Two examples are provided below.
Activity
C.Y.U. pages 285 - 287 #'s 53 - 68
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
Test Yourself
- Without graphing, tell what type of transformation would occur on the position vector (3 - 4i ) to obtain the resultant vector, if (3 - 4i ) is multiplied by 5i.
- Find each product or quotient below.
(a) (3 + 2i )(4 - 3i )
(b) (4 - 3i )2
(c) 
(d) 
(e) (2 + 5i )(2 - 5i )
Solutions
- The graph of 5i (3 - 4i ) is the graph of (3 - 4i ) rotated counterclockwise 90°, with a dilatation by a factor of 5.
