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Complex Numbers

Complex Numbers. Complex Numbers. Square root of a negative number- For any positive real number a, -a = i a. –169. For example: = 13i. –54 = –1 • 54. = –1 • 54. = i • 54. = i • 3 6. = 3 i 6. Complex Numbers. Lesson 5-6.

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Complex Numbers

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  1. Complex Numbers

  2. Complex Numbers Square root of a negative number- For any positive real number a, -a = i a –169 For example: = 13i

  3. –54 = –1 • 54 = –1 • 54 = i • 54 = i • 3 6 = 3i 6 Complex Numbers Lesson 5-6 Additional Examples Simplify –54 by using the imaginary number i.

  4. –121 – 7 = 11i – 7 Simplify the radical expression. Complex Numbers Lesson 5-6 Additional Examples Write –121 – 7 in a + bi (Complex Number) form. = –7 + 11iWrite in the form a + bi.

  5. Complex Numbers Lesson 5-6 Additional Examples Simplify the expression (3 + 6i) – (4 – 8i). (3 + 6i) – (4 – 8i) = 3 + (–4) + 6i + 8i Use commutative and associative properties. = –1 + 14i Simplify.

  6. Complex Numbers Lesson 5-6 Additional Examples Find each product. a. (3i)(8i) (3i)(8i) = 24i2Multiply the real numbers. = 24(–1)Substitute –1 for i2. = –24 Multiply. b. (3 – 7i)(2 – 4i) (3 – 7i)(2 – 4i) = 6 – 14i – 12i + 28i2 Multiply the binomials. = 6 – 26i + 28(–1) Substitute –1 for i2. = –22 – 26iSimplify.

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