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 |

Question

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 | (A) 22 (B) 32 (C) 38 (D) 42

Tardigrade Admin · Accepted Answer

The minimum value of above expression will exist for z=5ei α . For minimum of OP+PA+PB+PC+PD P must coincide with B . Hence the value of the given expression is 38 units <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-ibomcv88cxcm0dk0.jpg" />

Q. For any complex number $z$ in the largand plane, the minimum value of $∣ z ∣ + ∣ ∣ z - e^{i α} ∣ ∣ + ∣ ∣ z - 5 e^{i α} ∣ ∣ + ∣ ∣ z - 7 e^{i α} ∣ ∣ + ∣ ∣ z - 32 e^{i α} ∣ ∣$

$22$

$32$

$38$

$42$

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

Q. For any complex number z in the largand plane, the minimum value of ∣z∣+∣∣​z−eiα∣∣​+∣∣​z−5eiα∣∣​+∣∣​z−7eiα∣∣​+∣∣​z−32eiα∣∣​

22

32

38

42