MathDB
Problems
Contests
National and Regional Contests
Italy Contests
ITAMO
1985 ITAMO
3
3
Part of
1985 ITAMO
Problems
(1)
Some imaginary numbers
Source:
2/1/2006
Find
c
c
c
if
a
a
a
,
b
b
b
, and
c
c
c
are positive integers which satisfy
c
=
(
a
+
b
i
)
3
−
107
i
c=(a + bi)^3 - 107i
c
=
(
a
+
bi
)
3
−
107
i
, where
i
2
=
−
1
i^2 = -1
i
2
=
−
1
.
complex numbers