**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.