The greatest and least value of $\left|z_1+z_2\right|$  if $z_1=24+7i$  and $\left|z_2\right|=6$

$\left|z_1+z_2\right|\le \left|z_1\right|+\left|z_2\right|$

$=\left|24+7i\right|+6$

$=\sqrt{{\left(24\right)}^2+7^2}+6=25+6=31$

Also $\left|z_1+z_2\right|=\left|z_1-\left(-z_2\right)\right|$

$\ge \left|\left|z_1\right|-\left|z_2\right|\right|$ $=\left|25-6\right|=19$

$\therefore$  Least value = 19, Greatest value = 31

Hence option (1)