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Question

If z is a complex number such that |3z2|+|3z+2|=4, then the locus of z is

A
a line
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B
a circle
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C
a point
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D
a line segment
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Solution

The correct option is D a line segment
|3z2|+|3z+2|=4z23+z+23=43
Let A=(23,0), B=(23,0)
Then
|PA|+|PB|=|AB|
Hence, the locus of P is the line segment AB.

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