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College Algebra Chapter 1 Equations and Inequalities

College Algebra Chapter 1 Equations and Inequalities. Section 1.3 Complex Numbers. 1. Simplify Imaginary Numbers 2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers. Simplify Imaginary Numbers. and. If b is a positive real number, then.

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College Algebra Chapter 1 Equations and Inequalities

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  1. College AlgebraChapter 1Equations and Inequalities Section 1.3 Complex Numbers

  2. 1. Simplify Imaginary Numbers 2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers

  3. Simplify Imaginary Numbers and If b is a positive real number, then

  4. Examples 1 – 4: Write each expression in terms of i and simplify: 1. 2. 3. 4.

  5. Examples 5 – 7: Write each expression in terms of i and simplify: 5. 6. 7.

  6. Example 8: Multiply

  7. Example 9: Multiply

  8. Example 10: Divide

  9. 1. Simplify Imaginary Numbers 2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers

  10. Write Complex Numbers in the Form a + bi Given real numbers a and b, a number written in the form a + bi is called a complex number. a is the real part b is the imaginary part

  11. Examples 11 – 13: Simplify and write the result in standard form a + bi. 11. –5 12. 17i 13.

  12. Examples 14, 15: Simplify and write the result in standard form a + bi. 14. 15.

  13. 1. Simplify Imaginary Numbers 2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers

  14. Perform Operations on Complex Numbers Powers of i : Every fourth power of iequals 1.

  15. Perform Operations on Complex Numbers To simplify a power of i, write the expression as i to a power of 4 multiplied by .

  16. Examples 16 – 18: Simplify: 16. 18. 17.

  17. Perform Operations on Complex Numbers To add or subtract complex numbers, add or subtract their real parts, and add or subtract their imaginary parts.

  18. Examples 19, 20: 19. 20.

  19. Perform Operations on Complex Numbers Multiply complex numbers as you would multiply polynomials. Remember .

  20. Example 21:

  21. Example 22:

  22. Example 23:

  23. Example 24:

  24. Perform Operations on Complex Numbers The expressions a + bi and a – bi are called complex conjugates. The product of complex conjugates is a real number.

  25. Perform Operations on Complex Numbers To divide complex numbers, make the denominator a real number so the quotient can be written in the form a + bi.

  26. Example 25: Divide and write the result in the form a + bi.

  27. Example 26: Divide and write the result in the form a + bi.

  28. Example 27: Divide and write the result in the form a + bi.

  29. Example 28: Divide and write the result in the form a + bi.

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