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

(A) 1 (B) 0 (C) 1/2 (D) 3/2
Can you answer this question?

Toolbox:
• $|z_1|+|z_2|\geq|z_1-z_2|$
$|z|+|z-1|\geq|z-(z-1)|=1$
$\Rightarrow\:$ the least value of $|z|+|z-1|$ is $1$
answered Aug 1, 2013