Learning Resources
Lesson
This investigation begins with the simplification problem you were faced with before beginning Focus E. You were instructed, you may recall, to simplify the expression below.
As you saw, the simplification process was long and tedious. The solution would be simpler, however, if complex numbers in polar form were used. This is the intent of Investigation 4.
The Investigation is perhaps best done in pairs or small groups. Contact your on-line teacher for direction.
Proceed with the Investigation as outlined on pages 293 to 294 of your text. Hints and suggestions are provided for various steps. Use them only if you are experiencing difficulty.
Note: Accuracy is important when converting complex numbers in rectangular form to polar form. Be as accurate as possible until all calculations have been completed.
Answer the Investigation Questions on pages 295 & 296.
A summary of the Investigation is provided. However, it is divided into four categories.
- Converting rectangular coordinates to polar coordinates
- Converting polar coordinates to rectangular coordinates
- Converting a complex number written in polar form to rectangular form
- Converting a complex number written in rectangular form, a + bi, to polar form
Notebook Entry: Record the meaning of r cis
. As well, record the procedure, along with an accompanying example, of the following:
- Converting rectangular coordinates to polar coordinates
- Converting polar coordinates to rectangular coordinates
- Converting a complex number written in polar form to rectangular form
- Converting a complex number written in rectangular form, a + bi, to polar form
Activity
C.Y.U. page 297 #'s 23 - 26
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
- Write the rectangular coordinate
as a polar coordinate. - Give the rectangular coordinates of the polar coordinate (2, 540°).
- Convert 3 cos55° + 3i sin55° to a complex number expressed in rectangular form, a + bi.
- Express the complex number -2 - 3i in polar form.
Solutions
1. You want to get into the form (r, ).
2. You want to get (2, 540°) in the form (x, y).
3. 
4. -2 - 3i is the point (-2, 3) in the complex plane.
