MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2014 Harvard-MIT Mathematics Tournament
32
2014 Guts #32: A Classic System
2014 Guts #32: A Classic System
Source:
August 26, 2014
complex numbers
Problem Statement
Find all ordered pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of complex numbers with
a
2
+
b
2
≠
0
a^2+b^2\neq 0
a
2
+
b
2
=
0
,
a
+
10
b
a
2
+
b
2
=
5
a+\tfrac{10b}{a^2+b^2}=5
a
+
a
2
+
b
2
10
b
=
5
, and
b
+
10
a
a
2
+
b
2
=
4
b+\tfrac{10a}{a^2+b^2}=4
b
+
a
2
+
b
2
10
a
=
4
.
Back to Problems
View on AoPS