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Lesson 2.1, page 266 Complex Numbers

Lesson 2.1, page 266 Complex Numbers. Objective: To add, subtract, multiply, or divide complex numbers. 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

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Lesson 2.1, page 266 Complex Numbers

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  1. Lesson 2.1, page 266Complex Numbers Objective: To add, subtract, multiply, or divide complex numbers.

  2. 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

  3. Read Example 1, page 267. • To add or subtract, combine like terms. • (3 + 5i) + (2 - 4i) • (4 - 6i) - (3 - 7i)

  4. Your turn. Check Point 1. • A) (5 – 2i ) + (3 + 3i ) • B) (2 + 6i ) – (12 – i )

  5. Multiplication When multiplying radicals with negatives, take the root first, then multiply.

  6. Example 2For binomials, use the distributive property or FOIL. (Don’t forget to substitute -1 for i 2.)

  7. Your turn. Check Point 2. • A) 7i (2 – 9i ) • B) (5 + 4i ) (6 – 7i )

  8. Complex Conjugates • When dividing, we cannot leave a complex number in the denominator. • If binomial, multiply by it’s conjugate to simplify.

  9. Example 3, page 269.Find the conjugate. Multiply.

  10. Divide.

  11. Your turn. Check Point 3. • 5 + 4i 4 - i

  12. 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,…

  13. Practice with Roots of Negatives

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