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If `z` is any complex number such that `|z+4|lt=3,` then find the greatest value of `|z+1|dot`

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`|z + 1 | = |z + 4 - 3 |`
` = |( z + 4) + (-3)|` ltBrgt ` le |z + 4| + |-3|`
` = |z + 4| + 3 `
` le 3 + 3 = 6" " [ because |z + 4| le 3]`
Hence, the greatest value of ` |z + 1 |` is 6.
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