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Chapter 5.9

Chapter 5.9. Complex Numbers. Objectives. To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary solutions. To add, subtract, and multiply complex numbers. Why is this important?

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Chapter 5.9

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  1. Chapter 5.9 Complex Numbers

  2. Objectives • To simplify square roots containing negative radicands. • To solve quadratic equations that have pure imaginary solutions. • To add, subtract, and multiply complex numbers. Why is this important? You can use complex numbers to solve problems involving electricity and physics.

  3. Definition of Pure Imaginary Numbers For any positive real number b, =  or bi, where i is the imaginary unit, and bi is called a pure imaginary number

  4. Example 3x2 + 15 = 0 Answer: x = ± i i =

  5. Simplify Answer: 2i

  6. Example Simplify: i25 Answer: i

  7. Example Solve: 4x2 + 26 = 0 Answer: x = ±3i

  8. Definition of Equal Complex Numbers a + bi = c + di if and only if a = c and b = d Two complex numbers are equal is and only is their real parts are equal and their imaginary parts are equal.

  9. Examples Simplify the expression: (8 – 5i)+ (2 + i) Answer: 10 – 4i Simplify: (4 + 2i)(3 – 5i) Answer: 22 – 14i

  10. Practice p. 314 numbers 6-18 (even)

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