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

Know: modulus(z) < 3

WTS: |Im(z^{2}- z_{bar}+ 6)| <12

where z_{bar}is the complex conjugate

2. Relevant equations

z = x + iy

3. The attempt at a solution

|Im(z^{2}- z_{bar}+ 6)|

= |Im(x^{2}+ 2i*x*y - y^{2}- x + iy + 6)|

= |2xy + y|

So I want to show |2xy + y|< 12

I already proved it using maximization and Lagrange multipliers, but it seems like overkill, and I think there is some kind of arithmetic trick I am missing. Anyone see it?

Thanks

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# Homework Help: Complex numbers, basic problem

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