Chapter 12

  1. 1. (3 −  − 4) + (5 − 9 − 1) = (3 − 2j) + [ 5(3j) − 1]  = 3 − 2j + 15j − 1 = 2 + 13j

  2. 2. (2 ∠ 130 ° _ )(3 ∠ 45 ° _ ) = (2)(3) ∠ 130 ° _  + 45 °  = 6 ∠ 175 ° _ 

  3. 3. 2 − 7j : r = 22 + ( − 7)2 = 53 = 7.28tan θ =  − 72 =  − 3.500 , θref = 74.1 °  , θ = 285.9 ° 2 − 7j = 7.28(cos 285.9 °  + jsin 285.9 ° ) = 7.28 ∠ 285.9 ° _ 

  4. 4.

    1.  −  − 64 =  − (8j) =  − 8j

    2.  − j15 =  − j12j3 = ( − 1)( − j) = j

  5. 5. (4 − 3j) + ( − 1 + 4j) = 3 + j

    Three position vectors with heads connected by dashed segments. Vector 4 minus 3 j goes to (4, negative 3); vector 3 plus j goes to (3, 1); vector negative 1 plus 4 j goes to (negative 1, 4).

  6. 6. 2 − 4j5 + 3j = (2 − 4j)(5 − 3j)(5 + 3j)(5 − 3j) = 10 − 26j + 12j225 − 9j2 = 10 − 26j − 1225 − 9( − 1) =  − 2 − 26j34 =  − 1 + 13j17

  7. 7. 2.56(cos 125.2 °  + jsin 125.2 ° ) = 2.56 e2.185j125.2 °  = 125.2π180 = 2.185

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