Learning Resources

Investigation 5: Patterns in Operations With Complex Numbers

Step B

Recall: To change a complex number into polar form, you must get it in the form
r cis. The following formulas must be applied.

As well, when determining the value of , you must bear in mind the quadrant in which the terminal arm of the angle lies.

An example is provided below, if you are still having difficulty.

Example 1

Change -3 + i into polar form.

Solution.

As well, when converting from rectangular form to polar form, make use of your knowledge of special triangles. That is:

Be sure to record each individual complex number in polar form in your notebook as you will need the numbers later when completing the Investigation Questions. It might be a good idea to set up a table, similar to the one below, in which to record the information.