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    For this question, I'm just wondering whether there is a much simpler way to solve for x and y rather than treating the 2 fractions separately and multiplying by the complex conjugates for each.
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    (Original post by As_Dust_Dances_)
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    For this question, I'm just wondering whether there is a much simpler way to solve for x and y rather than treating the 2 fractions separately and multiplying by the complex conjugates for each.
    In this case, yes there is.

    Move the 1/(1+2i) to the RHS via subtraction.

    Put the RHS over a common denominator and simplify.

    Invert both fractions and simplify the RHS.
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    First write

    \frac 1 {x+iy} = \frac{2i}{1 + 2i}

    Then multiply the top and bottom of the RHS by \frac 1{2i} ...might save a little time.
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    (Original post by jb444)
    First write

    \frac 1 {x+iy} = \frac{2i}{1 + 2i}

    Then multiply the top and bottom of the RHS by \frac 1{2i} ...might save a little time.
    Unfortunately I don't have the answer at hand, but I'm getting x = 1 and y = -1/2 (is this correct from your calculations?)
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    (Original post by As_Dust_Dances_)
    Unfortunately I don't have the answer at hand, but I'm getting x = 1 and y = -1/2 (is this correct from your calculations?)
    Yes.
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    (Original post by ghostwalker)
    Yes.
    Thanks for your help
 
 
 
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