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

Question

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

Answer 1

Given |z + 4| ≤ 3

For greatest value of |z + 1|,

⇒ |z + 1| = |z + 4 – 3|

⇒ |z + 1| ≤ |z + 4 – 3|

⇒ |z + 1| ≤ 3 + 3

⇒ |z + 1| ≤ 6

So, greatest value of |z + 1| is 6.

We know that least value of the modulus of a complex number is zero.

So, the least value of |z + 1| is zero.