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The greatest value of $\mid z_1+z_2\mid$ if $z_1=24+7i$ and $|z_2|=6$ is :

$\begin{array}{1 1}(A)\;31&(B)\;19\\(C)\;25&(D)\;\text{None}\end{array} $

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$\mid z_2\mid=6$ represents a circle of radius 6 centred at origin
$|z_1+z_2|=|z_2-(-24-7i)|$
Greatest value =Distance BC
$\Rightarrow \sqrt{(24)^2+(7)^2}+6$
$\Rightarrow 31$
Hence (A) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 

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