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Mathematics
Mathematics
Problem
Let
A
A
A
,
B
B
B
and
C
C
C
be three sets of complex numbers as defined below:
A
=
{
z
:
Im
(
z
)
≥
1
}
A = \{z : \operatorname{Im}(z) \ge 1\}
A
=
{
z
:
Im
(
z
)
≥
1
}
B
=
{
z
:
∣
z
−
2
−
i
∣
=
3
}
B = \{z : |z - 2 - i| = 3\}
B
=
{
z
:
∣
z
−
2
−
i
∣
=
3
}
C
=
{
z
:
Re
(
(
1
−
i
)
z
)
=
2
}
,
where
i
=
−
1
C = \{z : \operatorname{Re}((1 - i)z) = \sqrt{2}\}, \text{ where } i = \sqrt{-1}
C
=
{
z
:
Re
((
1
−
i
)
z
)
=
2
}
,
where
i
=
−
1
The number of elements in the set
A
∩
B
∩
C
A \cap B \cap C
A
∩
B
∩
C
, is a. 0 b. 1 c. 2 d.
∞
\infty
∞
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