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

Options

A. 0
B. 2
C. 7
D. 17

Answer

B

Explanation

We have,
`|z_(1)|=12 rArr z_(1)` is a variable point on the circle `|z|=12` and , `|z_(2)-(3+4i)|=5`
`rArr z_(2)` is a variable point on the circle `|z-(3+4i)|=5`.
Circles `|z|=12`and `|z-(3+4i)|=5` are drawn as shown in the Fig.

It is evident from the figure that `z_(1)` and `z_(2)` are the affixes of point P and Q respectively and
`"min"|z_(1)-z_(2)|=PQ=OP-OQ=12-10=2`.