Problem 1.
Let ,
,
,
be complex numbers such that
=
and
. Prove that
Problem 2:
(Vietnamese Mathematical Olympiad, 1996)
Find all positive real numbers x and y satisfying the system of equations:
Problem 3:
Let ,
,
be complex numbers. Prove that
if and only if
,
and
.
You are most welcome to send your comments, discuss, etc.
Nalin Pithwa.