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Question

If z is any complex number satisfying z-3-2i2, then the minimum value of 2z-6+5i is


A

2

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B

1

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C

3

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D

5

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Solution

The correct option is D

5


Explanation for the correct option.

Find the minimum value of 2z-6+5i.

The expression 2z-6+5i can be written as

2z-6+5i=2z-3+52i=2z-3-2i+2i+52i=2z-3-2i+92i

Now, for two complex number z1 and z2 the triangle inequality can be given as: z1-z2z1+z2.

So the minimum value of 2z-3-2i+92i is given as:

2z-3-2i+92i=2z-3-2i-92i=22-92|z-3-2i|2=2-52=2×52=5

So, the minimum value of 2z-6+5i is 5.

Hence, the correct option is D.


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