Monday, July 25, 2011

Practice problems with complex numbers a + bi


a] (4 + i) + (7 - i)
b] (4 + i) - (7 - i)
c] (7 - i) - (4 + i)
d] (4 + i) * (7 - i)
e] (4 + i) / (7 - i)
f] (7 - i) / (4 + i)

Answers in the comments.
   
at

1 comment:

  1. Prof. HubbardJuly 25, 2011 at 6:21 PM

    a] (4 + i) + (7 - i)

    Answer: 11

    b] (4 + i) - (7 - i)

    Answer: -3 + 2i

    c] (7 - i) - (4 + i)

    Answer: 3 - 2i

    d] (4 + i) * (7 - i)

    FOIL: 28 - 4i + 7i - i^2 =

    28 - 4i + 7i + 1 =

    Answer: 29 + 3i

    e] (4 + i) / (7 - i)
    Multiply by (7 + i)/(7 + i)

    Numerator FOIL = 28 + 4i + 7i + i^2 =
    28 + 4i + 7i - 1 =

    27 + 11i

    Denominator FOIL =
    49 + 7i - 7i - i^2 =

    49 + 7i - 7i + 1=
    50

    Answer: 27/50 + 11i/50


    f] (7 - i) / (4 + i)

    Multiply by (4 - i)/(4 - i)

    Numerator FOIL = 28 - 7i - 4i + i^2 =
    28 - 7i - 4i - 1 =
    27 - 11i

    Denominator FOIL =
    16 - 4i + 4i - i^2 =

    16 + 7i - 7i + 1=
    17

    Answer: 27/17 - 11i/17

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