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March 24, 2017

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Given Z = 2(cos 148° + isin 148°) and W = 5(cos 11° + isin 11°), find and simplify z/w.
10(cos 137° – isin 137°)
0.4(cos 137° + isin 137°)
0.4(cos 137° – isin 137°)
10(cos 137° + isin 137°)

  • Calculus - ,

    multiply top and bottom by the conjugate of the denominator, that is, multiply top and bottom by
    (cos11 - isin11)
    (I will skip the ° sign)

    expand and simplify to get

    (2/5) (cos148cos11 - icos148sin11 + isin148cos11 - i^2sin148sin11)/(cos^2 11 - i^2 cos^2 11)

    = (2/5) (cos148cos11 - cos148sin11 + i(sin148cos11 - cos148sin11)/ 1
    = .4( cos(148-11) + i(sin(148-11))
    = .4(cos 137 + sin137)
    which is one of the choices.

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