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National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
1972 Spain Mathematical Olympiad
4
4
Part of
1972 Spain Mathematical Olympiad
Problems
(1)
projections on sets on complex plane
Source: Spanish Mathematical Olympiad 1972 P4
12/5/2022
The following sets of points are considered in the plane:
A
=
{
A=\{
A
=
{
affixes of complexes
z
z
z
such that arg
(
z
−
(
2
+
3
i
)
)
=
π
/
4
}
(z - (2 + 3i))=\pi /4\}
(
z
−
(
2
+
3
i
))
=
π
/4
}
,
B
=
{
B =\{
B
=
{
affixes of complexes
z
z
z
such that mod
(
z
−
(
2
+
i
)
<
2
}
( z- (2 + i)<2\}
(
z
−
(
2
+
i
)
<
2
}
. Determine the orthogonal projection on the
X
X
X
axis of
A
∩
B
A \cap B
A
∩
B
.
complex numbers