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Home » #### \(72x^7y^18\) - Parker Core Knowledge

#### \(72x^7y^18\) - Parker Core Knowledge

📅 May 2, 2026 👤 scraface

May 02, 2026

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Solution: Use $ |z|^2 + |w|^2 = |z + w|^2 - 2 ext{Re}(z \overline{w})...
eq 13 - 2i $. So not conjugates. Correct method: Let $ z = x + yi $, $...
$ x + u = 2 $, $ y + v = 4 $,
$ (x + yi)(u + vi) = xu - yv + (xv + yu)i = 13 - 2i $.
$ xu - yv = 13 $,
$ xv + yu = -2 $.
From $ u = 2 - x $, $ v = 4 - y $. Substitute:
$ x(2 - x) - y(4 - y) = 13 \Rightarrow 2x - x^2 - 4y + y^2 = 13 $,
$ x(4 - y) + y(2 - x) = 4x - xy + 2y - xy = 4x + 2y - 2xy = -2 $.
First equation: $ -x^2 + y^2 + 2x - 4y = 13 $.

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