(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If z and w are complex numbers such that |z|<=1 and |w|<=1 then prove

[tex]\left| z+w \right| \leq \left| 1 + \overline{z} w \right| [/tex]

3. The attempt at a solution

I have reduced this to essentially

x^2+y^2 <= 1+(xy)^2.

It seems to me if both x and y are less than or equal to 1, then the inequality must hold. I can't think of how to prove this formally, though. Any help on how to do this would be appreciated.

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# Proving an inequality

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