If $z \in C$, then the minimum value of $|z|+|2 z-3|+|z-1|$ is

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Aicharya · Accepted Answer

$ \begin{aligned} & 	ext { }|z|+|2 z-3|+|z-1|=|z|+|3-2 z|+|z-1| \ & \geq|z+z-1+3-2 z| \quad\left[\because\left|z_1+z_2ight| \leq\left|z_1ight|+\left|z_2ight|ight] \ & \geq|2| \ & 	herefore 	ext { Minimum value of }|z|+|2 z-3|+|z-1| 	ext { is } 2 \end{aligned} $

If $z \in C$, then the minimum value of $|z|+|2 z-3|+|z-1|$ is

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