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Dividing Complex Numbers

Dividing Complex Numbers. Express in the form: a + bi. multiply numerator and denominator by the conjugate of 1 – 2 i. 1 + 2 i. Recall: multiplying conjugates from class lesson. Example:. ( a – bi )( a + bi ). (2 – 7 i )(2 + 7 i ). = a 2 + abi – abi – b 2 i 2. a. b.

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Dividing Complex Numbers

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  1. Dividing Complex Numbers Express in the form: a + bi multiply numerator and denominator by the conjugate of 1 – 2i 1 + 2i

  2. Recall: multiplying conjugates from class lesson Example: (a – bi)(a + bi) (2 – 7i)(2 + 7i) = a2 + abi – abi – b2i2 a b = 22 + 72 (i2 = –1) = a2 – b2i2 = 4 + 49 = a2 – b2(–1) = 53 = a2 + b2 The product of two conjugates is always a real number.

  3. Express in the form: a + bi multiply numerator and denominator by the conjugate of 3 + 2i 3 – 2i

  4. Express in the form: a + bi multiply numerator and denominator by the conjugate of i – i

  5. d) Determine the reciprocal of: 5 – 3i

  6. e) Solve for z: 2 – 5i = (4 + 2i)z

  7. f ) Determine the sum

  8. g) Solve for z: 3 – i = (2 – 5i)z

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