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The region of the complex plane for which |z - a|/|z + ~a| = 1 (Re(a) is not equal to 0) is, a)x-axis b)y-axis c)the straight line x=a d)none of these Which option is correct?? Please explain.

The region of the complex plane for which |z - a|/|z + ~a| = 1 (Re(a) is not equal to 0) is,
a)x-axis
b)y-axis
c)the straight line x=a
d)none of these
Which option is correct?? Please explain.

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1 Answers

Arun
25750 Points
5 years ago
Dear student
 
If we open this we get
 
|z – a| = |z+a|
 
 
hence z is a locus which is always at same distance from (a , 0) and ( – a, 0).
hence Z will be at perpendicular bisector of both points i.e. Y axis.
 
Hence option B is correct

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