## Multiplying Complex Numbers: (8-11i)(8-11i)

This article explores the multiplication of the complex number (8-11i) by itself.

### Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form **a + bi**, where:

**a**and**b**are real numbers**i**is the imaginary unit, defined as the square root of -1 (i² = -1)

### Multiplying Complex Numbers

To multiply complex numbers, we use the distributive property (or FOIL method) just like with binomials.

**Step 1:** Expand the product using the distributive property:

(8 - 11i)(8 - 11i) = 8(8 - 11i) - 11i(8 - 11i)

**Step 2:** Simplify by multiplying:

= 64 - 88i - 88i + 121i²

**Step 3:** Substitute i² with -1:

= 64 - 88i - 88i + 121(-1)

**Step 4:** Combine real and imaginary terms:

= (64 - 121) + (-88 - 88)i

**Step 5:** Simplify:

= **-57 - 176i**

### Conclusion

Therefore, the product of (8-11i) and itself, (8-11i)(8-11i), is **-57 - 176i**. This demonstrates the process of multiplying complex numbers and the resulting complex number in standard form.