Complex Numbers 1 1 Write Complex Numbers MM
Complex Numbers 1. 1 Write Complex Numbers MM 2 N 1 a, MM 2 N 1 b
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.
Properties of Radicals • Product property of radicals • Quotient property of radicals
Perfect Squares ONE MINUTE!!! x x² x 1 2 3 11 12 13 4 5 6 7 8 9 10 14 15 16 17 18 19 20 x²
Perfect Squares ONE MINUTE!!! x x² 1 2 3 1 4 9 11 12 13 121 144 169 4 5 6 7 8 9 10 16 25 36 49 64 81 100 14 15 16 17 18 19 20 196 225 256 289 324 361 400
Find the greatest perfect square factor! • • A. B. C. D. E. F. G. 24 42 56 18 27 68 400
• Simplify the expression = 4, -4 • What property is needed? The product property!
• Simplify the expression =± • What property is needed? The quotient property!
Simplify the expression. A. C. E. 4 B. D. 4
Worksheet • Odds ONLY! • Simplify # 1, 3, 5, 7 and 9. • First find the greatest perfect square factor, then simplify. • ANSWERS:
How can we solve ?
Worksheet • Do # 13, 15 • ANSWERS:
How can we solve ?
Worksheet • Do # 19, 21, 23, 25, 27, 29 • ANSWERS:
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!
Worksheet • Do # 31, 33, 35 • ANSWERS:
Multiplying Radicals • Use the product property of radicals and distribute.
Worksheet • Do # 39, 41, 43 • ANSWERS:
Dividing Radicals • Use Rationalizing the Denominator to simplify
Worksheet • Do # 45, 47, 49, 51 • ANSWERS:
Solving radical equations • How do we solve
Worksheet • Do # 55, 57, 59, 61 • ANSWERS: 53. {96} 59. {-5} 55. {5} 57. {-5} 61. {320}
Homework Worksheet even numbered problems
Unit 1 – Complex Numbers • Solve
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.
Write complex numbers in standard form
Write the complex number in standard form.
Textbook Page 4 # 13 – 15 # 16, 18, 22, 24, 26, 32
Find real numbers x and y to make the equation true. 4 x + 6 y = 8 + 18 x= y=
Find real numbers x and y to make the equation true. 4 x – 4 yi = 8 – 12 i 5 x + 3 yi = 10 + 18 i
Find real numbers x and y to make the equation true. 8 x + 8 yi = 16 + 24 i 2 x – 7 yi = -14 + 21 i
Textbook Page 4 #36, 38
Homework Textbook Page 4 #17 -45 odd
- Slides: 33