We know that $$|z_1+z_2|\ge||z_1|-|z_2||$$ What about: $$|z_1+z_2+\dots+z_n|\ge||z_1|-|z_2|-\dots-|z_n||$$ Is it correct to generalize the first inequality? How to prove it by induction? What I get is $$|z_1+z_2+\dots+z_m+z_{m+1}|\ge|z_1+z_2+\dots+z_m|-|z_{m+1}||$$ $z_n$ are complex numbers.
2026-05-14 08:42:25.1778748145
General form of the triangle inequality
46 Views Asked by user718578 https://math.techqa.club/user/user718578/detail AtRelated Questions in CALCULUS
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