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Exploring Imaginary and Complex Numbers

Learn about the imaginary unit i and operations with complex numbers. Simplify square roots of negative numbers, add, subtract, and multiply complex numbers. Practice and enhance your understanding of imaginary and complex numbers.

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Exploring Imaginary and Complex Numbers

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  1. EQ7: How do we learn about the imaginary unit i and about imaginary numbers like 3i? EQ8: How do we perform operations with complex numbers? Tuesday, 20181009Imaginary & Complex Number

  2. Tuesday, 20181009 Essential Questions EQ7: How do we learn about the imaginary unit i and about imaginary numbers like 3i? EQ8: How do we perform operations with complex numbers? Vocabulary: imaginary numbers, complex numbers Agenda Bridge Math • Store your phones • Find your seat • Bellwork: ACT • Calculator • EQ7 & EQ8 Imaginary and Complex Numbers • Exit Ticket • Remain in seat until bell rings. Teacher Dismisses NOT the bell. It’s always a great day to be a Wolverine! No Sleeping!

  3. ACT Question 1

  4. ACT Question 2

  5. ACT Question 3

  6. ACT Question 4

  7. ACT Question 5

  8. ACT ANSWER KEY

  9. To multiply imaginary numbers or an imaginary number by a real number, it is important first to express the imaginary numbers in terms of i.

  10. Vocabulary imaginary unit imaginary number complex number real part imaginary part complex conjugate

  11. Example 1A: Simplifying Square Roots of Negative Numbers Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

  12. Example 1B: Simplifying Square Roots of Negative Numbers Express the number in terms of i. Factor out –1. Product Property. Simplify. Express in terms of i. i

  13. Check It Out! Example 1a Express the number in terms of i. Factor out –1. Product Property. Product Property. Simplify. Express in terms of i.

  14. Check It Out! Example 1c Express the number in terms of i. Factor out –1. Product Property. Simplify. Multiply. Express in terms of i.

  15. 4.) 5.) -Express these numbers in terms of i. Simplify. 3.)

  16. You try… 6. 7. 8.

  17. Multiplying Replace the i2 = -1 9. 10. 11.

  18. Complex Numbers standard form a + bi imaginary real The complex numbers consist of all sums a + bi, where a and b are real numbers and i is the imaginary unit. The real part is a, and the imaginary part is bi.

  19. Add or Subtract 12. 13. 14.

  20. Multiplying & Dividing Complex Numbers

  21. REMEMBER: i² = -1 Multiply 1) 2)

  22. You try… 3) 4)

  23. Multiply 5)

  24. You try… 6)

  25. You try… 7)

  26. EQ7 and EQ8 Lesson Quiz Perform the indicated operation. Write the result in the form a + bi. 1. (2 + 4i) + (–6 – 4i) –4 2. (5 – i) – (8 – 2i) –3 + i 3. (2 + 5i)(3 – 2i) 4. 3 + i 16 + 11i 5. Simplify i31. –i

  27. EXIT TICKET

  28. EXIT TICKET

  29. The End Tuesday 20181009

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