If |z+4| ≤ 3, then maximum value of |z+1| is

Question

If |z+4| ≤ 3, then maximum value of |z+1| is (A) 4 (B) 10 (C) 6 (D) 0

Tardigrade Admin · Accepted Answer

|z+4| ≤ 3 represents the interior and boundary of the circle with center at -4 and radius equal to 3 . As -1 is an end point of a diameter of the circle, maximum possible value of |z+1| is 6 which is attained when z=-7. See Fig. 2.48

Q. If $∣ z + 4∣ \leq 3$ , then maximum value of $∣ z + 1∣$ is

4

10

6

0

$∣ z + 4∣ \leq 3$ represents the interior and boundary of the circle with center at -4 and radius equal to 3 . As -1 is an end point of a diameter of the circle, maximum possible value of $∣ z + 1∣$ is 6 which is attained when $z = - 7$ . See Fig. 2.48

Q. If ∣z+4∣≤3, then maximum value of ∣z+1∣ is

4

10

6

0

∣z+4∣≤3 represents the interior and boundary of the circle with center at -4 and radius equal to 3 . As -1 is an end point of a diameter of the circle, maximum possible value of ∣z+1∣ is 6 which is attained when z=−7. See Fig. 2.48

Q. If $∣ z + 4∣ \leq 3$ , then maximum value of $∣ z + 1∣$ is

$∣ z + 4∣ \leq 3$ represents the interior and boundary of the circle with center at -4 and radius equal to 3 . As -1 is an end point of a diameter of the circle, maximum possible value of $∣ z + 1∣$ is 6 which is attained when $z = - 7$ . See Fig. 2.48