1. Warm Up Simplify Solve SAT Review question
Dana walks from home to school at a rate of 5 mph. It takes her 2 hours
longer to walk home from school than it did to walk to school. If her total
walking time to and from school was 8 hours, what was Dana’s rate of
speed walking home from school?
a) b) c) d) e) 15

2. Section 5.4 Complex Numbers Essential Question
What is an imaginary number?

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

8. Adding and Subtracting complex numbers 1
Adding and Subtracting complex numbers 1. add or subtract the real parts 2. add or subtract the imaginary parts
Ex:
Ex:

9. You try!

10. Multiplying 1. Treat the i’s like a variable 2
Multiplying 1. Treat the i’s like a variable 2. Change any that are not to the first power
Ex:
Ex:

11. You try!

12. Conjugates
The conjugate of a complex number has the same real part and the opposite imaginary part
Ex. Find the conjugate of 5 + 3i
5 – 3i
Ex. Find the conjugate of 3 – 2i
3 + 2i

13. Imaginary numbers in the denominator
i’s cannot be in the denominator (like radicals)
To get rid of the i’s, multiply numerator and denominator by the conjugate
If there is only an imaginary part in the denominator, multiply by the same imaginary number

14. Example

16. You try!

17. Assignment Pg. 277: #17-21(odd), 29-33(odd), 37-41(odd), 47-51(odd), 57-61(odd), 65-69(odd), 92

18. Assessment
Concept circles