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For all complex numbers z1,z2 satisfying...

For all complex numbers `z_1,z_2` satisfying `|z_1|=12 and |z_2-3-4i|=5` the minimum value of `|z_1-z|2|` is

A

0

B

2

C

7

D

17

Text Solution

Verified by Experts

The correct Answer is:
B
We know `|z_1-z_2|=|z_1-(z_2-3-4i)-(3+4i)|`
`ge |z_1|-|z_2-3-4i|-|3+4i|`
`ge 12-5 -5 [ using |z_1-z_2|ge |z_1|-|z_2|]`
`therefore |z_1-z_2| le 2`
Alternate Solution
Clearly from the firgure `|z_1-z_2|` is minimum when `z_1,z_2` lie alon the diameter

`therefore |z_1-z_2|le C_2B-C_2A le 12-10 =2`
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IIT JEE PREVIOUS YEAR-COMPLEX NUMBERS-TOPIC 2 CONJUGATE AND MODULUS OF A COMPLEX NUMBER (OBJECTIVE QUESTION I)(Only one correct option )
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