Download Section 3.2 Complex Numbers

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…
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Complex Number System
Rational
Real
Integers
Whole
Natural
…-8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7…
Irrational
3.2 Complex
Numbers
Objective: define and use the imaginary unit i and add,
subtract, multiply complex numbers
• Find the square root of each number.
A.
−25
B.
−72
C.
−5 −9
Practice: Find the square root.
1.
4
3.   36
2.
 12
4. 2  54
Complex Numbers
• Standard form: 𝑎 + 𝑏𝑖
• a is the real part
• bi is the imaginary part
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:
1. Set the real parts equal to each other.
2. Set the imaginary parts equal to each other.
3. Solve each.
Practice: Find the values of x
and y that satisfy the equation.
5. x + 3i = 9 − yi
6. 9 + 4yi = −2x + 3i
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)
Example: Operations with Complex Numbers
Add or subtract. Write the answers in standard form.
(7 – 6i) – (3 – 6i)
13 – (2 + 7i) + 5i
Practice: Perform the operation.
Write the answer in standard form.
7. (9 – i) + (-6 + 7i)
8. (3 + 7i) – (8 – 2i)
Practice: Perform the operation.
Write the answer in standard form.
9. (4 + 2i) + (8 + 7i)
10. (3 + 7i) – (8 – 2i)
Multiplying Complex Numbers
• When multiplying complex
numbers, distribute or “FOIL” as
needed.
• Write the final answer in standard
form.
Example: Multiply
4𝑖 −6 + 𝑖
−24𝑖 + 4𝑖 2
***NOTE: 𝑖 2 is the same as −1
−24𝑖 + 4 −1
−4 − 24𝑖
Practice
(9 − 2𝑖)(−4 + 7𝑖)
Homework
• Operations with Complex
Numbers Worksheet