A) 6 and 0
B) 10 and 6
C) 4 and 3
D) None of these
Correct Answer: A
Solution :
We have \[|z+1|=|z+4-3|\] ...(i) Now \[|z+4-3|\le |z+4|+|-3|\le 3+3=6\] [Given \[|z+4|\le 3\] & \[|-3|=3\]] \[\therefore \,\,|z+1|\le 6\] Again \[|z+1|\,\,\ge \,\,0\] [modulus is always non- negative] \[\therefore \] Least value of \[|z+1|\] maybe zero, which occurs when \[z=-1,\]For \[z=-1,\]\[|z+4|=|-1+4|=3\] Which satisfies the given condition that \[|z+4|\,\,\ge \,\,3\] Hence, the least and the greatest values of \[|z+1|\] are 0 and 6
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