how do add/ subtract/multiply Complex numbers

1. Math 2 Warmup
Simplify all the way
−36
−9 + −25
(4𝑖)2
𝑥 + 2 𝑥 − 4

2. Complex numbers
Learning Objective:
Today we are getting good at adding,
subtracting, and multiplying complex numbers

3. What is a “complex” number?
• A complex number is a number with 2 parts:
a + bi
Real part imaginary part
Examples: - 2 + 3i , - 4 – 5i , 7 – 9i, etc…

4. How do we ADD or SUBTRACT complex
numbers?
•Combine like terms!!
(−2 − 3𝑖) + (6 − 4𝑖)
= 4 − 7𝑖
−2 − 3𝑖 − 6 − 4𝑖
= −2 − 3𝑖 + −6 + 4𝑖
Subtraction becomes the
opposite:
= −8 + 𝑖

5. You try
1.
2. 5 − 6𝑖 − (8 − 4𝑖)
(6 + 2𝑖) + (7 + 3𝑖)
Answers
1. 13 + 5𝑖
2. −3 − 2𝑖

6. How do we multiply complex numbers?
• We use the box method
• And remember that 𝑖2
= −1
Example: 4 + 2𝑖 (3 − 2𝑖)
4 +2i
3
-2i
12 6i
-8i -4i2
= 12 − 2𝑖 − 4𝑖2
12 − 2𝑖 + 4
16 − 2𝑖

7. Now you try.
• Use the box method
• And remember that 𝑖2
= −1
2 − 5𝑖 (4 + 3𝑖)
2 -5i
4
+3i
8 -20i
6i -15i2
= 8 − 14𝑖 − 15𝑖2
8 − 14𝑖 +15
23 − 14𝑖

8. Homework…
1. Work on the complex numbers worksheet.
2. Catch up on any missing assignments....
• Imaginary numbers
• Vertex Form of Parabola
• Echo quiz.
This is the last day to turn in any work before grades are due.
•