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Mathematics
Mathematics
Problem
Let
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
and
a
2
+
b
2
≠
0
a^2 + b^2 \neq 0
a
2
+
b
2
=
0
. Suppose
S
=
{
z
∈
C
:
z
=
1
a
+
i
b
t
,
t
∈
R
,
t
≠
0
}
S = \{z \in \mathbb{C} : z = \frac{1}{a+ib}t, t \in \mathbb{R}, t \neq 0\}
S
=
{
z
∈
C
:
z
=
a
+
ib
1
t
,
t
∈
R
,
t
=
0
}
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
. If
z
=
x
+
i
y
z = x + iy
z
=
x
+
i
y
and
z
∈
S
z \in S
z
∈
S
, then
(
x
,
y
)
(x, y)
(
x
,
y
)
lies on
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