If $| z - 2 + i | = 2,$ then the greatest value of $| z |$ are respectively

2 + \sqrt{5}

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2 - \sqrt{5}

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\sqrt{5} + 2

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Solution

The correct option is A $2 + \sqrt{5}$
Given, $| z - 2 + i | = 2,$ .....(1).
Now,
$| z | = | z - (2 - i) + (2 - i) | \leq | z - (2 - i) | + | (2 - i) |$
or, $| z | \leq 2 + \sqrt{5}$ [ Using (1)]
From this it is clear that the greatest value of $| z |$ is $2 + \sqrt{5}$ .

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