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10 November, 19:13

Solve for the real values of x and y in the equation yi (2x + ) = (1 - i) ^3

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  1. 10 November, 19:39
    0
    x = - 0.5

    y = 2

    Step-by-step explanation:

    As per the given question,

    We have

    yi (2x + i) = (1 - i) ³

    Expand it by using cubic identity

    Cubic Identity:

    (x-y) ³ = x³ + 3xy² - 3x²y - y³

    Therefore, we get

    yi (2x + i) = (1³ + 3i² - 3i - i³)

    2xy i + y i² = 1 - 3 - 3i + i

    (As i² = - 1)

    2xy i - y = - 2i - 2

    On comparing the real and imaginary parts on both side, we get

    2xy = - 2

    And

    y = 2

    Therefore,

    x = - 0.5

    Hence, the required value of x = - 0.5 and y = 2.
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