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    Simplify a Complex Expression

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    Suppose that f (z) = x2 - y2 - 2y + iּ(2x - 2xy), where z = x + iy. Use the expressions
    _ _
    x = (z + z) /2 and y = (z - z)/2i

    to write f (z) in terms of z, and simplify the result.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:10 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/simplify-complex-expression-32502

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    f (z) = x2 - y2 - 2y + iּ(2x - 2xy) = x^2 - y^2 - 2y + 2ix - 2ixy
    z = x + i.y
    bar(z) = <z> = x - i.y

    x^2 = (z + <z>)^2/4 = (z^2 + <z>^2 + 2.z.<z>)/4
    y^2 = (z - <z>)^2/4.i^2 = - (z^2 + ...

    Solution Summary

    A complex expression is simplified. All work is shown.

    $2.49

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