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

$\begin{array}{1 1}(A) \;0 \\(B)\;1 \\(C)\;2\\(D)\;4 \end{array}$

Let $z=x+iy$
$|z|+|z-1|=\sqrt{x^2+y^2}+\sqrt{(x-1)^2+y^2}$
The minimum value of $|z|+|z-1|$ is occured when $x=0$ and $y=0$ or
when $x=1\:\:and\:\:y=0$ which is$=1$ on either case
edited Jul 28, 2014