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Question

If |z+4|3, then find the greatest and least values of |z + 1|.

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Solution

Given that, |z+4|3

For the greatest value of |z + 1|

|z+1|=|z+43||z+4|+|3|=|z+43|3+3=|z+43|6

So, greatest value of |z + 1| = 6

For, now, least value of |z + 1|, we know that the least value of the modulus of a complex number is zero. So, the least value of |z + 1| is zero.


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