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Complex Numbers 1.3

Complex Numbers 1.3. Multiply and Divide Complex Numbers MM2N1b, MM2N1c, MM2N1d. IMPORTANT!!!. i = ? i² = ?. Write the expression as a complex number in standard form. 4i(6 + 2i) = (3 – 2i)(-1 + 4i) = (5 + 7i)(2 + i ) =. Write the expression as a complex number in standard form.

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Complex Numbers 1.3

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  1. Complex Numbers 1.3 Multiply and Divide Complex Numbers MM2N1b, MM2N1c, MM2N1d

  2. IMPORTANT!!! • i = ? • i² = ?

  3. Write the expression as a complex number in standard form. • 4i(6 + 2i) = • (3 – 2i)(-1 + 4i) = • (5 + 7i)(2 + i) =

  4. Write the expression as a complex number in standard form. • (-1 + 5i)(6 + 3i) • (6 – 8i)(2 + 2i)

  5. Complex conjugates • Two complex numbers of the form a + bi and a – bi are called complex conjugates. What's the complex conjugate of: 5 + 2i 6 – 4i 83 + 42i 333 – 9879i

  6. Who remembers Difference of Squares? • (x + 4)(x – 4) = ? x² - 16 • (x + 6)(x – 6) = ? x² - 36 • (x – 9)(x + 9) = ? x² - 81 • (x – 13)(x + 13) = ? x² - 169 • (x – y)(x + y) = ? x² - y² • (x + 2y)(x – 2y) = ? x² - 4y²

  7. Multiply the complex conjugates. • (4 + 3i)(4 – 3i)

  8. Multiply the complex conjugates. • (8 – 4i)(8 + 4i) • Anytime you multiply two complex conjugates, what do you get? a² + b² A real number! Every time!!!

  9. Practice Textbook page 13 Do # 1 – 4 Do # 5, 13, 19, 23

  10. Homework Textbook page 13: #12 – 38 even and #39

  11. And now to division………..

  12. This must be simplified! Why?

  13. Write the expression as a complex number in standard form.

  14. Textbook page 13 Do # 27, 29, 31, 33, 35, 37

  15. COPY THIS DOWN!!!! Always substitute -1 for i². Difference of squares (a + bi)(a – bi) = a² + b²

  16. Homework • Textbook p. 13 #28 – 38 even and # 39

  17. Then by using the Difference of Squares • (a + bi)(a – bi) = ? a² - b²i² BUT we know i² = ? i² = -1 Now simplify a² - b²i² by substituting i² = -1 a² + b² SO (a + bi)(a – bi) = a² + b²

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