the equation im(iz-2/z-1)+1=0 represent a part of circle having radius equal
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Step-by-step explanation:Im(
z−i
iz−2
)+1=0
Writing z=x+iy, we have
Im(
x+i(y−1)
ix−y−2
)+1=0
⇒Im(
x+i(y−1)
ix−y−2
×
x−i(y−1)
x−i(y−1)
)+1=0
⇒Im(
x
2
+(y−1)
2
ix
2
+i(y−1)(y+2)−x(y+2)+x(y−1)
)+1=0
⇒
x
2
+(y−1)
2
x
2
+y
2
+y−2
=−1
⇒x
2
+y
2
+y−2=−x
2
−y
2
+2y−1
⇒2x
2
+2y
2
−y−1=0
⇒x
2
+y
2
−
2
1
y−
2
1
=0
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