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Question

For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, the minimum value of |z1-z2|is


A

4

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B

3

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C

1

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D

2

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Solution

The correct option is D

2


Finding the minimum value of bold vertical line bold italic z subscript bold 1 bold minus bold italic z subscript bold 2 bold vertical line bold space:

Given, |z1|=12& |z2-3-4i|=5

Now, we know that z1-z2=z1-z2

Applying this rule,

|z2-3-4i|=5z2--3-4i=5z2-32+42=5z2-5=5z2=10

Now,

z1-z2=z1-z2=12-10z1-z2=2

Hence, correct option is (D)


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