AP EAMCET · Maths · Complex Number
If \(z \in C\), then the minimum value of \(|z|+|2 z-3|+|z-1|\) is
- A 2
- B 1
- C 3
- D 0
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { }|z|+|2 z-3|+|z-1|=|z|+|3-2 z|+|z-1| \\ & \geq|z+z-1+3-2 z| \quad\left[\because\left|z_1+z_2\right| \leq\left|z_1\right|+\left|z_2\right|\right] \\ & \geq|2| \\ & \therefore \text { Minimum value of }|z|+|2 z-3|+|z-1| \text { is } 2 \end{aligned} \]
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