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Let Z(1) and Z(2) be two complex numbers...

Let `Z_(1)` and `Z_(2)` be two complex numbers satisfying `|Z_(1)|=9` and `|Z_(2)-3-4i|=4`. Then the minimum value of `|Z_(1)-Z_(2)|` is

A

1

B

2

C

`sqrt(2)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`|z_(1)| = 9`, circle with centre `C_(1)(0,0)` and radius `r_(1) = 9`
`|z_(2) - 3- 4i| = 4`, circle with radius `r_(2) = 4` and centre `C_(2)` (3, 4)
`C_(1)C_(2) = |r_(1)-r_(2)|`
`:.` both circles touch each other internally
`:. |z_(1) - z_(2)|_("min") = 0`
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