Which of the following represents the equation of the line segment joining $z_{1} = 3 i$ and $z_{2} = 3 \sqrt{3} .$

| z - 3 i | + | z - 3 \sqrt{3} | = \sqrt{27}

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| z + 3 i | + | z + 3 \sqrt{3} | = \sqrt{27}

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| z - 3 i | + | z + 3 \sqrt{3} | = 6

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| z - 3 i | + | z - 3 \sqrt{3} | = 6

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Solution

The correct option is D $| z - 3 i | + | z - 3 \sqrt{3} | = 6$
$Given: z_{1} = 3 i and z_{2} = 3 \sqrt{3}$

The equation of the line segment joining $z_{1}$ and $z_{2}$ is represented by:
$| z - z_{1} | + | z - z_{2} | = | z_{1} - z_{2} |$
Putting in the values, we get:
$| z - 3 i | + | z - 3 \sqrt{3} | = | 3 i - 3 \sqrt{3} |$
$| z - 3 i | + | z - 3 \sqrt{3} | = 6$
Hence, the answer is (a).

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