## Simplifying Complex Expressions: A Step-by-Step Guide

This article will guide you through simplifying the complex expression: **(7 - 3i) + (x - 2i)² - (4i + 2x²)**. We'll break down each step to ensure a clear understanding of the process.

### Expanding the Expression

First, we need to expand the squared term:

**(x - 2i)² = (x - 2i)(x - 2i)**

Using the FOIL method (First, Outer, Inner, Last), we get:

**(x - 2i)² = x² - 2xi - 2xi + 4i²**

Remember that **i² = -1**, so we can substitute:

**(x - 2i)² = x² - 4xi - 4**

Now our expression becomes:

**(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)**

### Combining Like Terms

Next, we group the real and imaginary terms separately:

**(7 - 4) + (x² - 2x²) + (-3i - 4xi - 4i)**

Combining the coefficients:

**3 + (-x²) + (-7 - 4x)i**

### Final Result

Therefore, the simplified form of the expression (7 - 3i) + (x - 2i)² - (4i + 2x²) is:

**-x² + ( -7 - 4x)i + 3**

This expression is now in the standard form of a complex number, **a + bi**, where **a** is the real part and **b** is the imaginary part.