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If |z1-1|lt=,|z2-2|lt=2,|z(33)|lt=3, the...

If `|z_1-1|lt=,|z_2-2|lt=2,|z_(33)|lt=3,` then find the greatest value of `|z_1+z_2+z_3|dot`

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`|z_(1)+z_(2)+z_(3)|=|(z_(1)-1)+(z_(2)-2)+(z_(3)-3)+6|`
`le|z_(1)-1|+|z_(2)-2|+|z_(3)-3|+6`
`ge1+2+3+6=12`
Hence, the greatest value is 12.
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