Complex Numbers 1.1 Write Complex Numbers MM2N1a, MM2N1b.

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Presentation transcript:

Complex Numbers 1.1 Write Complex Numbers MM2N1a, MM2N1b

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!!! xx²x

Perfect Squares ONE MINUTE!!! xx²x

Find the greatest perfect square factor! A. 24 B. 42 C. 56 D. 18 E. 27 F. 68 G. 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. B. C.D. E. 44

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} 55. {5} 57. {-5} 59. {-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. 4x + 6y = x = y =

Find real numbers x and y to make the equation true. 4x – 4yi = 8 – 12i 5x + 3yi = i

Find real numbers x and y to make the equation true. 8x + 8yi = i 2x – 7yi = i

Textbook Page 4 #36, 38

Homework Textbook Page 4 #17-45 odd