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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
20
/
c
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
20
/
b
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
20
/
a
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
2
/
Solution
2026-10-18
View more
Write
−
8
=
8
e
i
(
π
+
2
πk
)
. Its three
roots
have
modulus
2
and arguments
(
π
+
2
πk
)
/3
, with
k
=
0
,
1
,
2
. Thus all three
complex roots
are
z
=
1
+
i
3
,
−
2
,
1
−
i
3
.
(1)
Further
integer
values of
k
repeat these
roots
.
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
19
/
c
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
19
/
b
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
19
/
a
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
18
/
d
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
18
/
c
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
18
/
b
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
18
/
a
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
f
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
e
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
d
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
c
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
b
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
17
/
a
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
16
/
b
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
16
/
a
2026-10-18
0
Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge
/
2015
/
Paper 2
/
15
/
b
2026-10-18
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