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

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

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Let $z=x+iy$
Min. value of $|z|+|z+1|=$ min. value of $\sqrt {x^2+y^2}+\sqrt {(x+1)^2+y^2}$
This is possible only when $x^2+y^2=0$ or $(x+1)^2+y^2=0$
In either case the min value is 1
answered Jul 22, 2013 by rvidyagovindarajan_1

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