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Question

The number of complex number(s) z satisfying |z3i|=|z9i| and |z3+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,
|z3i|=|z9i|
(x3)2+(y1)2=(x9)2+(y1)2
(x3)2+(y1)2=(x9)2+(y1)2
x=6
Now, |z3+3i|=3
(x3)2+(y+3)2=3
(x3)2+(y+3)2=9
For x=6, y=3.
z=63i

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