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Complex Numbers: Multiplying, Dividing , Graphing and Absolute Value

Complex Numbers: Multiplying, Dividing , Graphing and Absolute Value. Notes 16 - Section 4.6 b. Essential Learnings. Students will understand and be able to perform basic operations with complex numbers.

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Complex Numbers: Multiplying, Dividing , Graphing and Absolute Value

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  1. Complex Numbers:Multiplying, Dividing, Graphing and Absolute Value Notes 16 - Section 4.6 b

  2. Essential Learnings • Students will understand and be able to perform basic operations with complex numbers. • Students will understand and be able to graph complex numbers and find the absolute value.

  3. Summary of Complex Numbers Complex numbers: numbers that have areal part and animaginary part. Imaginary number (i) is defined as:

  4. Multiplying Complex Numbers Same as with variables except Example 1:

  5. Example 2 Simplify the complex number.

  6. Example 3 Simplify the complex number.

  7. Example 4 Simplify the complex number.

  8. Example 5 Simplify the complex number.

  9. Class Problems Simplify the complex numbers.

  10. Class Problems - Solutions

  11. No imaginary numbers in the denominator! Use conjugates to get a real number in the denominator. Dividing Complex Numbers

  12. Complex Conjugates • Two complex numbers of the form: • The product of complex conjugates is always a real number.

  13. Example 6 - Dividing Write the expression in standard form.

  14. Example 7 - Dividing Write the expression in standard form.

  15. Class Problems Write the expression in standard form.

  16. Class Example 1

  17. Class Example 2

  18. Graphing Complex Numbers Real Number Complex Number Coordinate Plane Coordinate Plane

  19. Graphing Complex Numbers

  20. Absolute Value of a Complex Number Absolute value is the distance from a number to zero on a number line. Absolute value of a complex is the distance from the complex number to the origin in the complex plane.

  21. Absolute Value of The absolute value of a complex number is denoted z.

  22. Example 8 Find the absolute value of the complex number.

  23. Example 9 Find the absolute value of the complex number.

  24. Example 10 Find the absolute value of the complex number.

  25. Class Problems Find the absolute value of the complex numbers.

  26. Assignment Page 280: 24 – 33 (x3), 35 – 55 odd, 60 Unit Study Guide 2

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