1. 3.2 Complex Numbers

2. 16th Century mathematicians pondered this question:
= ????

3. Example 1
Simplify

4. Product of square roots

5. Example 2
Simplify:

6. A complex number written in standard form is a number a + bi where a and b are real numbers.
real part
imaginary part
If b ≠ 0, then a + bi is an imaginary number.
If a = 0 and b ≠ 0, then a + bi is a pure imaginary number.

7. Complex Numbers a + bi Imaginary Numbers Real Numbers
Remember: every real number is a complex number, and so is every pure imaginary number.

8. Example 3
Solve the following equation for x and y:
Set the real parts equal to each other and imaginary parts equal to each other:

9. Example 4
Set the real parts equal to each other and imaginary parts equal to each other:

10. Add or subtract. Write answer in standard form.
Example 5
Add or subtract. Write answer in standard form.

11. Multiplying complex numbers
Example 6
Multiplying complex numbers

12. Finding Zeros of a Quadratic Function
Example 7
Finding Zeros of a Quadratic Function