Multiple Choice Questions on The locus of a complex variable z satisfying z 1 z 1 2 is ........ for NDA Exam Preparation

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Multiple Choice Questions

The locus of a complex variable z satisfying z 1 z 1 2 is ........

Mathematics (NDA) Complex Numbers
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    The locus of a complex variable z satisfying |(z -1)/(z+1)| = 2 is ? 

    Circle

    Correct Answer

    Line 

    Incorrect Answer

    Parabola 

    Incorrect Answer

    None of these  

    Incorrect Answer
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    Explanation:

    Given ,   

    |(z-1)/(z+1)| = 2 

    ⇒    | (x+ i y -1)/(x+ i y +1)|=2 

    ⇒    |(x-1) +i y|2 / |(x+1) + i y|2 = 4 

    ⇒    (x -1)2 + y2 = 4(x+1)2 + 4y2 

    ⇒     3x2 + 3y2 + 10x +3 = 0 

    ⇒     3(x2 +y2) + 10x+3 = 0 ,  

    which is a circle . 

                            

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