A) one
B) two
C) four
D) none of these
Correct Answer: A
Solution :
[a]: Let\[z=x+iy\]. Then,\[|z-3-i|=|z-9-i|\] \[\Rightarrow \]\[\sqrt{{{(x-3)}^{2}}+{{(y-1)}^{2}}}=\sqrt{{{(x-9)}^{2}}+{{(y-1)}^{2}}}\] \[\Rightarrow \]\[x=6\] Also,\[|z-3+3i|=3\]\[\Rightarrow \]\[\sqrt{{{(x-3)}^{2}}+{{(y+3)}^{2}}}=3\] For\[x=6,y=-3.\therefore z=6-3i\] \[\therefore \]There is only one complex number.
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