Complex Numbers 1.1

1
Complex Numbers 1.1

• Write Complex Numbers
• MM2N1a, MM2N1b

2
Vocabulary Review

• Square Root
• A number r is a square root of a number s
• if r² s.
• Radical
• The expression is called a radical. The
  symbol is a radical sign.
• Radicand
• The number s beneath the radical sign.

3
Properties of Radicals

• Product property of radicals
• Quotient property of radicals

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Perfect SquaresONE MINUTE!!!
x x² x x²
1 11
2 12
3 13
4 14
5 15
6 16
7 17
8 18
9 19
10 20
5
Perfect SquaresONE MINUTE!!!
x x² x x²
1 1 11 121
2 4 12 144
3 9 13 169
4 16 14 196
5 25 15 225
6 36 16 256
7 49 17 289
8 64 18 324
9 81 19 361
10 100 20 400
6
Find the greatest perfect square factor!

• A. 24
• B. 42
• C. 56
• D. 18
• E. 27
• F. 68
• G. 400

7

• Simplify the expression
• 4, -4
• What property is needed?
• The product property!

8

• Simplify the expression
• What property is needed?
• The quotient property!

9
Simplify the expression.

• A. B.
• C. D.
• E.

4
4
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Worksheet

• Odds ONLY!
• Simplify 1, 3, 5, 7 and 9.
• First find the greatest perfect square factor,
  then simplify.
• ANSWERS

11
How can we solve ?
12
Worksheet

• Do 13, 15
• ANSWERS

13
How can we solve ?
14
Worksheet

• Do 19, 21, 23, 25, 27, 29
• ANSWERS

15
Adding and Subtracting Radicals

• If we have one square root of three and add two
  square roots of three to it, how many square
  roots of three do we have?
• NOTE We can only combine radicals with the same
  radicands.

Prove this with a calculator!
16
Worksheet

• Do 31, 33, 35
• ANSWERS

17
Multiplying Radicals

• Use the product property of radicals and
  distribute.

18
Worksheet

• Do 39, 41, 43
• ANSWERS

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Dividing Radicals

• Use Rationalizing the Denominator to simplify

20
Worksheet

• Do 45, 47, 49, 51
• ANSWERS

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Solving radical equations

• How do we solve

22
Worksheet

• Do 55, 57, 59, 61
• ANSWERS
• 53. 96 55. 5 57. -5
• 59. -5 61. 320

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Homework

• Worksheet even numbered problems

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Unit 1 Complex Numbers

• Solve

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Vocabulary

• Imaginary Unit i
• i where i² -1.
• Complex Number
• Written in standard form a bi where a and b are
  real numbers. The number a is the real part and
  the number bi is the imaginary part.
• Imaginary Number
• If b ? 0, then a bi is an imaginary number.
• Pure Imaginary Number
• If a 0 and b ? 0, then a bi is a pure
  imaginary number.

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Write complex numbers in standard form
27
Write the complex number in standard form.
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Textbook

• Page 4 13 15
• 16, 18, 22, 24, 26, 32

29
Find real numbers x and y to make the equation
true.

• 4x 6y 8 18
• x y

30
Find real numbers x and y to make the equation
true.

• 4x 4yi 8 12i
• 5x 3yi 10 18i

31
Find real numbers x and y to make the equation
true.

• 8x 8yi 16 24i
• 2x 7yi -14 21i

32
Textbook

• Page 4
• 36, 38

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Homework

• Textbook
• Page 4 17-45 odd