## Solving the Equation (x^2 + 4)^2 = 0

This equation may seem a bit intimidating at first glance, but it's actually quite simple to solve. Let's break it down step by step:

### Understanding the Equation

The equation (x² + 4)² = 0 represents a **squared term** being set equal to zero. This means that the expression inside the parentheses must also be equal to zero.

### Solving for x

**Take the square root of both sides:**√(x² + 4)² = √0**Simplify:**x² + 4 = 0**Isolate x²:**x² = -4**Take the square root of both sides:**x = ±√(-4)**Simplify:**x = ±2i (where 'i' is the imaginary unit, √-1)

### The Solution

The solutions to the equation (x² + 4)² = 0 are **x = 2i** and **x = -2i**. These are **complex numbers**, as they involve the imaginary unit 'i'.

### Key Takeaways

**Squaring an expression sets it to zero only if the expression itself is zero.****The square root of a negative number results in an imaginary number.**

This problem demonstrates the importance of understanding the properties of exponents and the concept of imaginary numbers when working with equations.