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  4. The greatest and the least value of |z1 + z2| if z1 =24+7i and |z2|=6 respectively are

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Q. The greatest and the least value of $\left|z_{1} + z_{2}\right|$ if $z_{1}$ $=24+7i$ and $\left|z_{2}\right|=6$ respectively are

NTA AbhyasNTA Abhyas 2022

Solution:

$z_1+z_2 \leq z_1+z_2=|24+7 i|+6=25+6=31$
Also, $z_1+z_2=z_1--z_2 \geq \| z_1|-| z_2||$
$\Rightarrow z_1+z_2 \geq|25-6|=19$
Hence the least value of $z_1+z_2$ is $19$ and the greatest value is $31 $.