Search any question & find its solution
Question:
Answered & Verified by Expert
If $z \in C$, then the minimum value of $|z|+|2 z-3|+|z-1|$ is
Options:
Solution:
1859 Upvotes
Verified Answer
The correct answer is:
2
$$
\begin{aligned}
& \text { }|z|+|2 z-3|+|z-1|=|z|+|3-2 z|+|z-1| \\
& \geq|z+z-1+3-2 z| \quad\left[\because\left|z_1+z_2\right| \leq\left|z_1\right|+\left|z_2\right|\right] \\
& \geq|2| \\
& \therefore \text { Minimum value of }|z|+|2 z-3|+|z-1| \text { is } 2
\end{aligned}
$$
\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}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.