## Squaring Complex Numbers: (5-4i)^2

This article explores the process of squaring the complex number (5-4i).

### 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 (5-4i)

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

(5-4i)^2 = (5-4i)(5-4i)

Now, we can expand this using the distributive property (FOIL method):

= 5(5-4i) - 4i(5-4i) = 25 - 20i - 20i + 16i^2

Since i^2 = -1, we can substitute:

= 25 - 20i - 20i - 16 = 9 - 40i

### Conclusion

Therefore, (5-4i)^2 = **9 - 40i**.

This result demonstrates the process of squaring complex numbers and how the imaginary unit 'i' interacts within these calculations.