## Squaring Complex Numbers: (7-2i)²

This article will walk through the process of squaring the complex number (7-2i).

### Understanding Complex Numbers

Complex numbers are numbers 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.

### Squaring (7-2i)

To square (7-2i), we simply multiply it by itself:

(7-2i)² = (7-2i)(7-2i)

We can use the **FOIL** method (First, Outer, Inner, Last) to expand the product:

**First:**7 * 7 = 49**Outer:**7 * -2i = -14i**Inner:**-2i * 7 = -14i**Last:**-2i * -2i = 4i²

Combining the terms, we get:

49 - 14i - 14i + 4i²

Remember that **i² = -1**. Substituting this into our expression:

49 - 14i - 14i + 4(-1)

Simplifying:

49 - 14i - 14i - 4

Combining real and imaginary terms:

**(49 - 4) + (-14 - 14)i**

Finally, we arrive at the solution:

**(7-2i)² = 45 - 28i**

### Conclusion

Squaring a complex number involves expanding the expression and simplifying the result, using the knowledge that i² = -1. The result of (7-2i)² is **45 - 28i**.