2. GEOMETRIC REPRESENTATION OF COMPLEX NUMBERS A Complex Number is in the form: z = a+bi We can graph complex numbers on the axis shown below: Real axis Imaginary Axis

3. ABSOLUTE VALUE OF A COMPLEX NUMBER An arrow is drawn from the origin to represent the complex number. The length of the arrow is the absolute value of the complex number.

4. REPRESENTING COMPLEX NUMBERS USING RECTANGULAR VS. POLAR COORDINATES So, We abbreviate this as cis

5. Complex Numbers Rectangular Form: Polar Form:

6. Example: Convert to rectangular form. Formulas:

7. Example: Convert to polar form. Formulas:

8. Example: What is the absolute value of the following complex numbers:

9. Multiply:

10. Do you want to go thru that every time? No!

11. Multiply:

12. Divide:

13. SUMMARY To convert a+bi to polar: To convert to rectangular: Formulas: Formulas: