Question

If $|z+i|\le 2$, then the maximum value of $|z+12+6i|$ is

• A. 12
• B. 24
• C. 15
• D. 14

Answer 1

The correct option is C

15

$|z+i|=2$ is a circle with centre -i and radius 2. $|z+i|\le 2$ represents the region inside this circle and on the circle.

$|z+12+6i|$ is the distance of Z from -12 -6i.

The maximum value of $|z+12+6i|$ is AD and minimum value is BD.

AD=AC+CD

AC=2

CD=|-12-6i-(-i)|

= $\sqrt{{12}^2+5^2}$

= 13

∴ AD= 2+13

=15 Or,

$|z+12+6i|$ = $|z+i+12+5i|$

$|z+12+6i|$ = $|z+i|+|12+5i|$

$\le 2+13$

$\le 15$