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Question: Answered & Verified by Expert
If z=a+ib satisfies arg(z-1)=arg(z+3i), then (a-1):b=
MathematicsComplex NumberJEE Main
Options:
  • A 2:1
  • B 1:3
  • C -1:3
  • D None of these
Solution:
1493 Upvotes Verified Answer
The correct answer is: 1:3

We have,

arg(z-1)=arg(z+3i)

arg((a-1)+ib)=arg(a+(b+3)i)

tan-1ba-1=tan-1b+3a

 ba-1=b+3a

 ab=(a-1)(b+3)

 3(a-1)=b

 (a-1):b=1:3

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