The number of complex number(s) z satisfying |z−3−i|=|z−9−i| and |z−3+3i|=3 is
A
one
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
two
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
four
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
infinitely many
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
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