## Expanding (8-2i)^2

This article will explore the expansion of the complex number (8-2i)^2.

### Understanding Complex Numbers

Complex numbers are numbers of the form **a + bi**, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, defined as **√-1**.

### Expanding the Expression

To expand (8-2i)^2, we can use the FOIL method (First, Outer, Inner, Last):

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

**First:**8 * 8 = 64**Outer:**8 * -2i = -16i**Inner:**-2i * 8 = -16i**Last:**-2i * -2i = 4i^2

Now we combine the terms and remember that i^2 = -1:

64 - 16i - 16i + 4(-1) = 64 - 32i - 4

Finally, we simplify the expression:

**(8-2i)^2 = 60 - 32i**

### Conclusion

Therefore, the expansion of (8-2i)^2 results in the complex number **60 - 32i**. This process demonstrates how to expand complex numbers by using the FOIL method and applying the fundamental property of the imaginary unit, i^2 = -1.