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Question

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

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Solution

|z+1|=|z+43|=|(z+4)+(3)||z+4|+|3|=|z+4|+33+3=6 [|z+4|3]
Hence, the greatest value of |z+1| is 6.
Ans: 6

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