I step with a inequality and would like to know if it is truth...
$||(a_1-a_2)^2+i(b_1-b_2)^2||\leq ||a_1^2+ib_1^2||+||a_2^2+ib_2^2||,\quad \forall a_1,a_2\in\mathbb{R}$.
I tried to prove it but couldn't. Any help will be appreciated.
2026-03-27 01:14:00.1774574040
Inequality within complex
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It's wrong.
Try $a_1=b_1=1$ and $a_2=b_2=-1$.