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Iran MO (3rd Round)
2023 Iran MO (3rd Round)
2
Complex FE
Complex FE
Source: Iran MO 2023 3rd round , Algebra exam P2
August 21, 2023
function
algebra
Problem Statement
find all
f
:
C
→
C
f : \mathbb{C} \to \mathbb{C}
f
:
C
→
C
st:
f
(
f
(
x
)
+
y
f
(
y
)
)
=
x
+
∣
y
∣
2
f(f(x)+yf(y))=x+|y|^2
f
(
f
(
x
)
+
y
f
(
y
))
=
x
+
∣
y
∣
2
for all
x
,
y
∈
C
x,y \in \mathbb{C}
x
,
y
∈
C
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