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  4. For z ∈ C if the minimum value of (| z -3 √2|+| z - p √2 i |) is 5 √2, then a value of p is

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Q. For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______

JEE MainJEE Main 2022Complex Numbers and Quadratic Equations

Solution:

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$ \sqrt{(3 \sqrt{2})^2+( p \sqrt{2})^2}=5 \sqrt{2}$
$18+2 p ^2=50$
$ p ^2=16 $
$p =\pm 4$
As per option $( C )$ is correct