Exercises 12.3, page 353

  1. 1. 3 − j

    A graph of 3 vectors that extends from the origin. Two dashed vectors extend into quadrant 2 and quadrant 4. The sum extends into quadrant 4.

  2. 3.

    A graph with a point plotted 2 units right, 6 units up.

  3. 5.

    A graph with a point plotted 4 units left, 3 units down.

  4. 7.  − 3j

    A graph with a point plotted 0 units left or right, 3 units down.

  5. 9. 5 + 4j      

    The graph of 3 vectors from the origin. One is along the positive x-axis, another is in quadrant 1, and another is solid and between them in quadrant 1. Dashed lines connect the terminal ends.

  6. 11. 8 + j

    The graph of 3 vectors from the origin. One is in quadrant 4, another is in quadrant 1, and another is solid and between them in quadrant 1. Dashed lines connect the terminal ends.

  7. 13.  − 1 + 9j

  8. 15.  − 3j      

  9. 17.  − 1 + 4j

  10. 19.  − 

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