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(C) The expression $|z-3 \sqrt{2}| + |z-p \sqrt{2} i|$ represents the sum of the distances of a complex number $z$ from the points $A(3 \sqrt{2}, 0)$

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$4$

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(C) The expression $|z-3 \sqrt{2}| + |z-p \sqrt{2} i|$ represents the sum of the distances of a complex number $z$ from the points $A(3 \sqrt{2}, 0)$ and $B(0, p \sqrt{2})$ in the complex plane.The minimum value of the sum of distances from two points is the distance between the two points themselves,which is the length of the line segment $AB$.Given that the minimum value is $5 \sqrt{2}$,we have $AB = 5 \sqrt{2}$.The distance formula between $A(3 \sqrt{2}, 0)$ and $B(0, p \sqrt{2})$ is given by $\sqrt{(3 \sqrt{2} - 0)^2 + (0 - p \sqrt{2})^2} = 5 \sqrt{2}$.Squaring both sides,we get $(3 \sqrt{2})^2 + (p \sqrt{2})^2 = (5 \sqrt{2})^2$.$18 + 2p^2 = 50$.$2p^2 = 32$.$p^2 = 16$.$p = \pm 4$.Thus,a possible value of $p$ is $4$.

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

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