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Question

A complex function
f(z)=u+iv is defined as f(z)=ziz+1 where z=x+iy then the imaginary part of f(z) is

A
x2+y2+xyx2+y2+2x+1
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B
yx1x2+y2+2x+1
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C
1x2+y2+1
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D
x2+y2x2+y2+1
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Solution

The correct option is B yx1x2+y2+2x+1
f(x+iy)=x+iyix+iy+1
=[x+i(y1)][x+1iy](x+1)2+y2=x2+y2+xy+i(yx1)x2+y2+2x+1
Imag(f(x+iy))=yx1x2+y2+2x+1

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