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Question

If the ratio 1z1+z is purely imaginary, then

A
|z|1/2
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B
|z|=1
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C
|z|>1
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D
0<|z|<1
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Solution

The correct option is B |z|=1
Let w=1z1+z
Since, w is purely imaginary.
Therefore, w+¯w=0
1z1+z+1¯z1+¯z=0
(1z)(1+¯z)+(1¯z)(1+z)=0
|z|2=1
|z|=1
Ans: B

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