Q. 25 H5.0( 3 Votes )
Fill in the blanks of the following
If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ……… and …….
Answer :
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.
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