If |z + 4|, le ,3, then greatest and least value of |z + 1| are

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4-1.Complex numbers

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If $|z + 4|\, \le \,3,$ then the greatest and the least value of $|z + 1|$ are

A

$6, -6$

B

$6, 0$

C

$7, 2$

D

$0, -1$

Solution

(b) $|z + 4|\, \le 3$==> $ – 3 \le z + 4 \le + 3$

==> $ – 6 \le z + 1 \le 0$==> 0$ \le – (z + 1) \le 6$

==> $0 \le \,|z + 1| \le 6$,

Hence greatest and least values of $|z + 1|$ are $6$ and $0$ respectively.

Standard 11

Mathematics

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