## Squaring Complex Numbers: A Step-by-Step Guide for (8-3i)^2

This article will guide you through the process of squaring the complex number (8-3i).

### 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 (8-3i)

To square (8-3i), we simply multiply it by itself:

**(8-3i)^2 = (8-3i) * (8-3i)**

To perform this multiplication, we can use the **FOIL** method:

**F**irst: 8 * 8 = 64**O**uter: 8 * -3i = -24i**I**nner: -3i * 8 = -24i**L**ast: -3i * -3i = 9i^2

Remember that i^2 = -1, so we can simplify the last term:

9i^2 = 9(-1) = -9

Now, we combine the terms:

64 - 24i - 24i - 9 = **55 - 48i**

### Conclusion

Therefore, (8-3i)^2 is equal to **55 - 48i**. By following the steps outlined above, you can confidently square any complex number.