Learning Resources

Focus C: Adding and Subtracting Complex Numbers

Step F

If you are unsure as to whether or not Stephanie is correct, use an example to check. An easy example to use, of course, is the one given in the previous steps.

1. Find the modulus of 5 + 2i.
2. Find the modulus of 3 - 4i.
3. Add the two moduli.
4. Find the modulus of 8 - 2i.
5. Compare your answer to the sum obtained in step 3. Are they the same or different?

This process can also be illustrated graphically by following the procedure below.

1. Illustrate (5 + 2i ) and (3 - 4i ).
2. Illustrate the sum graphically.
3. Determine the value of the resultant vector.
4. Examine the triangle formed by three vectors. Is the length of the resultant vector equal to the sum of the two other vectors? Why or why not?

You should recall that the sum of the two smallest sides of a triangle must be greater than the biggest side.