2. 11.2a Geometric Representation of a Complex Number Write complex numbers in polar form.

3. 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 Argand Diagram

4. 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.

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

6. Complex Numbers Rectangular Form: Polar Form:

7. Convert to Rectangular Formulas:

8. Convert to Polar Form

9. Absolute Value of a Complex Nubmer ( Magnitude) Same as a radius!!!!!

10. Homework 11.2 P. 406 1-12 all

11. 11.2b Complex Numbers Expressing Products and Quotient’s of Complex Numbers in Polar and Rectangular Form.

12. Operations with complex numbers

13. Do you want to go thru that every time?

14. Multiply:

15. How do you think we can work with division?

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

18. Homework Pg. 406, 17-21odd, 23, 24