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Question

The number of complex numbers z that satisfies both the equation |z1i|=2 and |z+1+i|=2, is

A
1
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B
2
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C
4
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D
infinite
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Solution

The correct option is B 2
|z1i|=2
This represents a circle with centre, C1(1,1) and radius r1=2

|z+1+i|=2
This represents a circle with centre, C2(1,1) and radius r2=2

Now, C1C2=22+22=22
r2+r1=2+2r2r1=22
So, r2+r1>C1C2>r2r1
Therefore, these two circles intersect at two points only.
Hence, there are two possible complex numbers satisfying the given equations.

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