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For any complex number $z$, the minimum value of $|z|+|z-1|=?$

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  • $|z_1|+|z_2|\geq|z_1-z_2|$
$|z|+|z-1|\geq|z-(z-1)|=1$
$\Rightarrow\:$ the least value of $|z|+|z-1|$ is $1$
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