## Simplifying Complex Numbers: (5 - 2i)²

This article will guide you through the process of simplifying the complex number expression (5 - 2i)².

### Understanding Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1.

### Expanding the Expression

To simplify (5 - 2i)², we can use the FOIL method (First, Outer, Inner, Last) or simply expand it like a binomial squared:

(5 - 2i)² = (5 - 2i)(5 - 2i)

Expanding:

(5 - 2i)(5 - 2i) = 5(5) + 5(-2i) - 2i(5) - 2i(-2i)

### Simplifying the Terms

Simplify the multiplication:

25 - 10i - 10i + 4i²

Since i² = -1, substitute it:

25 - 10i - 10i + 4(-1)

Combine the real and imaginary terms:

(25 - 4) + (-10 - 10)i

### Final Result

The simplified form of (5 - 2i)² is:

**(21 - 20i)**