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The least value of |z-3-4i|^(2)+|z+2-7i|...

The least value of `|z-3-4i|^(2)+|z+2-7i|^(2)+|z-5+2i|^(2)` occurs when z=

A

A. `1+3i`

B

B. `3+3i`

C

C. `3+4i`

D

D. None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Let `z=x+iy`
Then `|z-3-4i|^(2)+|z+2-7i|^(2)+|z-5+2i|^(2)`
`=3(x^(2)+y^(2)-4x-6y)+107`
`=3[{(x-2)^(2)+(y-3)^(2)]+68`
`:.` The least value occurs when `x=2` and `y=3`
`:.z=2+3i`
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