1. Complex Numbers
Lesson 1.3 day1 Notes

2. Complex Numbers Learning Target: Students will be able to…
Identify imaginary numbers and their place in the number system
Rewrite negative radicals as complex numbers
Simplify products and quotients involving radicals of negative numbers

3. It's any number you can imagine
The Imaginary Number i
By definition
Consider powers if i

4. Using i
Now we can handle quantities that occasionally show up in mathematical solutions
What about

5. Complex Numbers Combine real numbers with imaginary numbers Examples
a + bi
Examples
Real part
Imaginary part

6. The set of Complex Numbers

7. VENN DIAGRAM Representation
Since all number belong to the Complex number field, C, all number can be classified as complex. The Real number field, R, and the imaginary numbers, i, are subsets of this field as illustrated below.
Complex Numbers
a + bi
Real Numbers
a + 0i
Imaginary Numbers
0 + bi

8. Try It Out
Write these complex numbers in standard form a + bi

11. Complex Numbers on the Calculator
Possible result
Reset mode Complex format to Rectangular
Now calculator does desired result

12. Complex Numbers on the Calculator
Operations with complex on calculator
Make sure to use the correct character for i. Use 2nd-i

13. Warning Consider It is tempting to combine them
The multiplicative property of radicals only works for positive values under the radical sign
Instead use imaginary numbers

14. Try It Out
Use the correct principles to simplify the following:

15. Assignment
HW 1.3 #1-5, (all), (even)