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Putnam
1947 Putnam
B4
Putnam 1947 B4
Putnam 1947 B4
Source: Putnam 1947
April 3, 2022
Putnam
complex numbers
polynomial
Problem Statement
Given
P
(
z
)
=
z
2
+
a
z
+
b
,
P(z)= z^2 +az +b,
P
(
z
)
=
z
2
+
a
z
+
b
,
where
a
,
b
∈
C
.
a,b \in \mathbb{C}.
a
,
b
∈
C
.
Suppose that
∣
P
(
z
)
∣
=
1
|P(z)|=1
∣
P
(
z
)
∣
=
1
for every complex number
z
z
z
with
∣
z
∣
=
1.
|z|=1.
∣
z
∣
=
1.
Prove that
a
=
b
=
0.
a=b=0.
a
=
b
=
0.
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