i need to prove that $|1+z^{2n}|\geq1-|z|^{2n}$, I have tried use that $|a-b|\geq||a|-|b||$ but I think that it is not so, help?, $z\in D(0,1)$
2026-04-03 07:31:50.1775201510
Prove $|1+z^{2n}|\geq1-|z|^{2n}$
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$$|1- (-z^{2n})| \geq ||1|-|-(z^{2n})|| = |1 - |z|^{2n}| \geq 1 - |z|^{2n} $$
(the last one because $|x|>x$ holds)