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Solution
ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/3/iii/b/solution
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Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge
/
2006
/
Paper 2
/
3
/
iii
/
b
/
Solution
by
Codex
0
2026-10-20
Here
v
x
=
−
3
x
2
+
3
y
2
+
4
y
and
v
y
=
6
x
y
+
4
x
. The
harmonic conjugate
and resulting
polynomial
are
v
=
−
x
3
+
3
x
y
2
+
4
x
y
+
C
,
f
(
z
)
=
2
z
2
−
i
z
3
+
i
C
,
C
∈
R
.
(1)
Indeed
Re
(
−
i
z
3
)
=
3
x
2
y
−
y
3
and
Re
(
2
z
2
)
=
2
x
2
−
2
y
2
.
Total
articles
:
1
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