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  4. For any complex number z in the largand plane, the minimum value of |.z|.+|z - ei α |+|z - 5 ei α |+|z - 7 ei α |+|z - 32 ei α |

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Q. For any complex number $z$ in the largand plane, the minimum value of $\left|\right.z\left|\right.+\left|z - e^{i \alpha }\right|+\left|z - 5 e^{i \alpha }\right|+\left|z - 7 e^{i \alpha }\right|+\left|z - 32 e^{i \alpha }\right|$

NTA AbhyasNTA Abhyas 2022

Solution:

The minimum value of above expression will exist for $z=5e^{i \alpha }$ .
For minimum of $OP+PA+PB+PC+PD$
$P$ must coincide with $B$ .
Hence the value of the given expression is $38$ units
Solution