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Suppose that z is a complex number the s...

Suppose that `z` is a complex number the satisfies `|z-2-2i|lt=1.` The maximum value of `|2i z+4|` is equal to _______.

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The correct Answer is:
3
`|z-2-2i| le 1`
denotes the region inside a circle with center (2,2) and radius is 1.

`|2iz + 4|=|2i(z-2i)|`
`=|2i| |z-2i|`
`= 2|z-2i|`
`|z-2i|`= distance of z form `P(0,2)`
Hence,maximum value is 3.
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