1. Groups Today Group 1: Myles, Kaitlyn, Victoria
Group 2: Matthew, William, Emily
Group 3: Darius, Vanessa
Group 4: Jorge, Mariana, Anthony
Group 5: Ryan, Julio, Moises
Group 6: Anthony G., Le’ona, Ariadny

2. Complex Numbers

3. Imaginary Unit
Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can!
The imaginary unit is ¡ ¡=
It is used to write the square root of a negative number.

4. Property of the square root of negative numbers
If r is a positive real number, then
Examples:

5. *For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead.
Example:

6. Examples

7. Complex Numbers Example: 5+4i Real part Imaginary part
A complex number has a real part & an imaginary part.
Standard form is:
Real part
Imaginary part
Example: 5+4i

8. The Complex plane
Real Axis
Imaginary Axis

9. Graphing in the complex plane

10. Adding and Subtracting (add or subtract the real parts, then add or subtract the imaginary parts)
Ex:
Ex:
Ex:

11. Multiplying Treat the i’s like variables, then change any that are not to the first power
Ex:
Ex:

13. Partner Showdown
You will complete the problem on their own, and reveal the answer to one-another at the same time.
If your group all has the same answer, you may move on.
If you do not, you must discuss any errors and work together to clear-up any misunderstandings before moving on.

14. Next class You will have a quiz on this material next class.
Be sure to complete your homework!

15. Exit Ticket