Complex Numbers Practice and Operations

Exploring complex numbers, including defining and using the imaginary unit, finding square roots, solving equations for real and imaginary parts, and performing operations such as addition and subtraction. Practice exercises and examples help reinforce understanding of these mathematical concepts.

• Complex Numbers
• Practice
• Operations
• Equations

dom_r Follow

Uploaded on Sep 26, 2024 | 0 Views

Download Presentation

Please find below an Image/Link to download the presentation.

The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.

Presentation Transcript

1. 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. Complex Number System Rational Real 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 A. 72 B. C. 5 9

5. Practice: Find the square root. 4 36 1. 3. 2 12 54 4. 2.

6. Complex Numbers Standard form: ? + ?? 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: 1. Set the real parts equal to each other. 2. Set the imaginary parts equal to each other. 3. Solve each.

8. Practice: Find the values of x and y that satisfy the equation. 5. x + 3i = 9 yi 6. 9 + 4yi = 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) 8. (3 + 7i) (8 2i)

12. Practice: Perform the operation. Write the answer in standard form. 9. (4 + 2i) + (8 + 7i) 10. (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 4? 6 + ? 24? + 4?2 ***NOTE: ?2 is the same as 1 24? + 4 1 4 24?

15. Practice (9 2?)( 4 + 7?)

16. Homework Operations with Complex Numbers Worksheet