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Lesson 2.1, page 266 Complex Numbers Objective: To add, subtract, multiply, or divide complex numbers.
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VOCABULARY & Properties Imaginary unit -- the number i Note: This is used to take the square root of negative numbers. Complex Numbers -- numbers of the form a + bi (a is “real”, b is “imaginary”) Example: 2 + 3i or 4 - 7i
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Read Example 1, page 267. To add or subtract, combine like terms. (3 + 5i) + (2 - 4i) (4 - 6i) - (3 - 7i)
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Your turn. Check Point 1. A) (5 – 2i ) + (3 + 3i ) B) (2 + 6i ) – (12 – i )
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Multiplication When multiplying radicals with negatives, take the root first, then multiply.
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Example 2 For binomials, use the distributive property or FOIL. (Don’t forget to substitute -1 for i 2.)
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Your turn. Check Point 2. A) 7i (2 – 9i ) B) (5 + 4i ) (6 – 7i )
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Complex Conjugates When dividing, we cannot leave a complex number in the denominator. If binomial, multiply by it’s conjugate to simplify.
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Example 3, page 269. Find the conjugate. Multiply.
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Divide.
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Your turn. Check Point 3. 5 + 4i 4 - i
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Review of Simplifying Radicals Know the perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225,…,400, 625, 900, 1000,…
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Practice with Roots of Negatives
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