The number of complex number(s) z satisfying |z−3−i|=|z−9−i| and |z−3+3i|=3 is
A
one
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B
two
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C
four
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D
infinitely many
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Solution
The correct option is A one Let z=x+iy. Then, |z−3−i|=|z−9−i| ⇒√(x−3)2+(y−1)2=√(x−9)2+(y−1)2 ⇒(x−3)2+(y−1)2=(x−9)2+(y−1)2 ⇒x=6
Now, |z−3+3i|=3 ⇒√(x−3)2+(y+3)2=3 ⇒(x−3)2+(y+3)2=9
For x=6,y=−3. ∴z=6−3i