## Squaring Complex Numbers: (8 + 7i)²

This article will explore the process of squaring the complex number (8 + 7i).

### 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.

### Squaring a Complex Number

To square a complex number, we simply multiply it by itself. In this case, we have:

(8 + 7i)² = (8 + 7i)(8 + 7i)

### Expanding the Product

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

(8 + 7i)(8 + 7i) = 8(8) + 8(7i) + 7i(8) + 7i(7i)

Simplifying the terms:

= 64 + 56i + 56i + 49i²

### Remembering i² = -1

Since i² is defined as -1, we can substitute:

= 64 + 56i + 56i - 49

### Combining Real and Imaginary Terms

Finally, combining the real and imaginary terms:

= **(64 - 49) + (56 + 56)i**

= **15 + 112i**

### Conclusion

Therefore, (8 + 7i)² is equal to **15 + 112i**. This demonstrates how to square a complex number and how to simplify the result by combining real and imaginary terms.