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Previous Practice:

   Example 1: 5(2 + 3i)
                             multiply by real 
                             nu...
Imaginary Number x Complex Number

   Example 1: i(3 + 4i)




   Example 2: 4i(2 - 3i)




                              ...
Complex Number x Complex Number

   Example 1: (5 + 3i)(2 + 4i)




   Example 2: (-2 + 5i)(3 - i)




                   ...
Multiplying Conjugates

   Example 1: (3 + 2i)(3 - 2i)




   Example 2: (-5 - i)(-5 + i)




                            ...
General Rule When Multiplying Conjugates:

       (a + bi)(a - bi) =




                                            5
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Algebra 2 Notes 2-7

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Multiplying Complex Numbers

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Algebra 2 Notes 2-7

  1. 1. Previous Practice: Example 1: 5(2 + 3i) multiply by real  number:  changes length  Example 2: -2(3 - 4i) of vector 10+15i multiply by ­1: rotate 180 1
  2. 2. Imaginary Number x Complex Number Example 1: i(3 + 4i) Example 2: 4i(2 - 3i) multiply by i: rotate 90 2
  3. 3. Complex Number x Complex Number Example 1: (5 + 3i)(2 + 4i) Example 2: (-2 + 5i)(3 - i) 3
  4. 4. Multiplying Conjugates Example 1: (3 + 2i)(3 - 2i) Example 2: (-5 - i)(-5 + i) 4
  5. 5. General Rule When Multiplying Conjugates: (a + bi)(a - bi) = 5

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