Question

If |z+4|<= 3,then find maximum value of |z+1| (here <= signify less than and is equal to)?

Answer 1

Maximum value of `|z+1|` is `6`.

Explanation:

`|z+4|<=3` represents all points in a circle, whose center `(-4,0)` and radius is `3` including those on circumference.

graph{(x+4)^2+y^2<=9 [-11, 3, -3.5, 3.5]}

`|z+1|` denotes moving this circle to right by one unit.

graph{(x+3)^2+y^2<=9 [-11, 3, -3.5, 3.5]}

Maximising `|z+1|` means farthest point from origin i.e. `(-6,0)`

and hence maxima is for `6+i0` and its value is `sqrt((-6)^2+0^2)=6`