## Squaring a Complex Number: (5 + i)^2

This article will explore the process of squaring the complex number (5 + i).

### 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 (i.e., **i² = -1**).

### Squaring the Complex Number

To square (5 + i), we simply multiply it by itself:

**(5 + i)² = (5 + i)(5 + i)**

We can expand this using the distributive property (or FOIL method):

**(5 + i)(5 + i) = 5 * 5 + 5 * i + i * 5 + i * i**

Simplifying:

**= 25 + 5i + 5i + i²**

Since i² = -1, we can substitute:

**= 25 + 5i + 5i - 1**

Combining real and imaginary terms:

**= (25 - 1) + (5 + 5)i**

**= 24 + 10i**

### The Result

Therefore, the square of (5 + i) is **24 + 10i**.

This demonstrates how squaring a complex number involves multiplying it by itself and utilizing the property that i² = -1 to simplify the expression.