1. real, whole, natural, rational, irrational, integers
Do Now: Fill in the blanks with the following words:
real, whole, natural, rational, irrational, integers
________
____
_______
________
_______
_________
…-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7…

2. Real Complex Number System Rational Integers Whole Irrational Natural
Integers
Whole
Irrational
Natural
…-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7…

3. 3.2 Complex Numbers
Objective: define and use the imaginary unit i and add, subtract, multiply complex numbers

4. Find the square root of each number.
−25
−72
−5 −9

5. Practice: Find the square root.1. 3. 2. 4.

6. Complex Numbers Standard form: 𝑎+𝑏𝑖 a is the real part
bi is the imaginary part

7. Two complex numbers a + bi and c + di are equal if and only if a = c and b = d.
Find the values of x and y that satisfy the equation: 2x − 7i = 10 + yi
Steps:
Set the real parts equal to each other.
Set the imaginary parts equal to each other.
Solve each.

8. Practice: Find the values of x and y that satisfy the equation.
5. x + 3i = 9 − yi yi = −2x + 3i

9. Operations with Complex Numbers
To add (or subtract) two complex numbers, add (or subtract) their real parts and their imaginary parts separately.
*It might help to highlight like terms.
Add or subtract. Write the answers in standard form.
(8 – i) + (5 + 4i)

10. Example: Operations with Complex Numbers
Add or subtract. Write the answers in standard form. (7 – 6i) – (3 – 6i) 13 – (2 + 7i) + 5i

11. Practice: Perform the operation. Write the answer in standard form.
7. (9 – i) + (-6 + 7i) (3 + 7i) – (8 – 2i)

12. Practice: Perform the operation. Write the answer in standard form.
9. (4 + 2i) + (8 + 7i) (3 + 7i) – (8 – 2i)

13. Multiplying Complex Numbers
When multiplying complex numbers, distribute or “FOIL” as needed.
Write the final answer in standard form.

14. Example: Multiply
4𝑖 −6+𝑖 −24𝑖+4 𝑖 2 ***NOTE: 𝑖 2 is the same as −1 −24𝑖+4 −1 −4−24𝑖

15. Practice
(9−2𝑖)(−4+7𝑖)

16. Homework
Operations with Complex Numbers Worksheet