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Question

The locus of z satisfying the inequality log13|z+1| > log13|z-1| is


A

R(z)<0

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B

R(z)>0

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C

I(z)<0

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D

None of these

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Solution

The correct option is A

R(z)<0


We know that logam>logan m>n or m<n, according as a>1 or 0<a<1

Hence for z=x+iy

log13|z-1| |z+1|<|z-1|

{o<13<1}

|x+iy+1|<|x+iy-1|

(x+1)2 + y2<(x1)2 + y2

4x<0 x<0 Re(z)<0


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