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Question

The complex number z satisfying the equation |zi|=|z+1|=1 is

A
0
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B
1+i
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C
1+i
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D
1i
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Solution

The correct options are
A 0
C 1+i
Let z=x+iy
|zi|=|z+1|=1

|zi|=|z+1|
x2+(y1)2=(x+1)2+y2
x2+y22y+1=x2+2x+1+y2x=y (1)

|z+1|=1
(x+1)2+x2=1 [From (1)]2x2+2x=0x(x+1)=0
x=0,1
y=0,1

z=0,1+i

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