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Question

The possible integral values of k for which the equation
|z+i||zi|=k,k>0 represents a hyperbola is

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Solution

|zz1||zz2|=k represent hyperbola if k<|z1z2|
So, |z+i||zi|=k represents hyperbola if k<|i(i)|
k<2
0<k<2 (k>0)
Clearly, only 1 integral value is possible.

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