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Question

If z be a complex number satisfying |z|+2¯¯¯z=z, then complete solution set of z lies on-

A
the positive real axis including orgin
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B
the positive real axis
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C
the negative imaginary axis including origin
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D
the negative real axis including origin
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Solution

The correct option is D the negative real axis including origin
Here |z|+2¯¯¯z=z .........(i)
Taking conjugate
|z|+2z=¯¯¯z ........(ii)
subtracting equation 1 and 2 we get,
z=¯¯¯z zR
|z|+z=0 z0
z lies on negative real axis including origin.

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