Show that the equation represent a circle, and find its centre and radius. |3z − 2 − i| = 3
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Answer:
Let z=x+iy. Then,
∣
z−3
z−2
∣=2
∣
(x−3)+iy
(x−2)+iy
∣=2
∣(x−2)+iy∣=2∣(x−3)+iy∣
(x−2)
2
+y
2
=2
(x−3)
2
+y
2
(x−2)
2
+y
2
=4[(x−3)
2
+y
2
]
3x
2
+3y
2
−20x+32=0
x
2
+y
2
−
3
20
x+
3
32
=0
(x−
3
10
)
2
+(y−0)
2
=(
3
2
)
2
, which represents a circle with centre at (
3
10
,0) and radius
3
2
.
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