Algebra I Part IIY - Administration



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Complex Numbers

UNIT QUESTION: In what ways can algebraic methods be used in problems solving? MCC9-12.N.RN.1-3, .1-3, A.APR.1

Today’s Question: How do we take the square root of negative numbers?

MCC9-12..1-3

[pic]

|[pic] |

Examples:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

[pic]

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|Always divide the exponent by 4. |

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|If it divides evenly, then the answer is 1. |

|If you get a remainder of 1 or 0.25, then the answer is [pic] |

|If you get a remainder of 2 or 0.50, then the answer is [pic] |

|If you get a remainder of 3 or 0.75, then the answer is [pic] |

Examples:

5. [pic]

6. [pic]

7. [pic]

8. [pic]

9. [pic]

Add and Subtract Complex Numbers

← Add or subtract the real parts, and then, add or subtract the imaginary parts.

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

[pic]

Multiplying Complex Numbers

← Treat the [pic]’s like variables, then change any that are not to the first power.

Examples:

15. [pic]

16. [pic]

17. [pic]

18. [pic]

19. [pic]

20. [pic]

[pic]

Conjugates

← Two complex numbers of the form a + bi and a – bi are complex conjugates.

← The product is always a real number.

Example [pic]

[pic]

Dividing Complex Numbers

← Multiply the numerator and denominator by the conjugate of the denominator.

← Simplify completely.

Examples:

Write each expression as a complex number in standard form.

1. [pic]

20. [pic]

21. [pic]

22. [pic]

23. [pic]

24. [pic]

Complex Numbers – Practice

[pic]

Write each expression in standard form.

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

7. [pic]

8. [pic]

[pic]

9. [pic]

10. [pic]

11. [pic]

12. [pic]

13. [pic]

14. [pic]

15. [pic]

[pic]

16. [pic]

17. [pic]

18. [pic]

[pic]

19. Which has the same value as [pic]?

a. -2i b. -2 c. 2 d. 2i

20. Let r = (4 + i) and s = 1 – i. What is the value of r2 – s?

a. 14 + i b. 15 + I c. 15 + 7i d.14 + 9i

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