Divide the following complex numbers: (2 + i) \div (1 - 4i)

Question

Divide the following complex numbers:
(2 + i) \div (1 - 4i)

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Thành Công 4 years 2021-07-31T21:36:55+00:00 1 Answers 7 views 0

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    2021-07-31T21:38:48+00:00

    Answer:

    -\dfrac{2}{17} + \dfrac{9}{17}i

    Step-by-step explanation:

     (2 + i) \div (1 - 4i) =

     = \dfrac{2 + i}{1 - 4i}

     = \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i}

     = \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)}

     = \dfrac{2 + 8i + i + 4i^2}{1 + 16}

     = \dfrac{2 + 9i - 4}{17}

     = \dfrac{-2 + 9i}{17}

    = -\dfrac{2}{17} + \dfrac{9}{17}i

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )