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Math Help - complex numbers inequality

  1. #1
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    complex numbers inequality

    i get everything until the red line, why is the next step like that? and where did the part on top of the green line come from?

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  2. #2
    o_O
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    |x|^{2} - 2|x||y| + |y|^{2} \geq 0
    \Rightarrow |x|^{2} + |y|^{2} \geq 2|x| |y| ..........................................(Moved 2|x||y| to right side)
    \Rightarrow |x|^{2} + |y|^{2} {\color{red} + |x|^{2} + |y|^{2}} \geq 2|x| |y| {\color{red} + |x|^{2} + |y|^{2}}..........(Added |x|^2 + |y|^2 to both sides)
    \Rightarrow 2|x|^{2} + 2|y|^{2} \geq |x|^{2} + 2|x||y| + |y|^{2}......................(Simplified)
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