## Squaring a Complex Number: (-1 - 2i)²

This article will demonstrate how to square the complex number **(-1 - 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 a Complex Number

To square a complex number, we simply multiply it by itself:

(-1 - 2i)² = (-1 - 2i) * (-1 - 2i)

### Expanding the Product

We can expand this product using the FOIL method (First, Outer, Inner, Last):

**First:**(-1) * (-1) = 1**Outer:**(-1) * (-2i) = 2i**Inner:**(-2i) * (-1) = 2i**Last:**(-2i) * (-2i) = 4i²

### Simplifying the Expression

Now we have: 1 + 2i + 2i + 4i²

Remember that i² = -1. Substituting this in:

1 + 2i + 2i + 4(-1) = 1 + 2i + 2i - 4

Combining real and imaginary terms:

(1 - 4) + (2 + 2)i = **-3 + 4i**

### Conclusion

Therefore, (-1 - 2i)² = **-3 + 4i**. This is another complex number, demonstrating that squaring a complex number can result in another complex number.