Algebra I Part IIY - Administration
Name: ________________________________________________ Date: _______________________
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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