## Multiplying Complex Numbers: (7 + 5i)(8 - 6i)

This article will guide you through multiplying the complex numbers (7 + 5i) and (8 - 6i).

### Understanding Complex Numbers

Complex numbers are numbers 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 (**i² = -1**).

### Multiplication of Complex Numbers

To multiply complex numbers, we treat them like binomials and use the distributive property (or the FOIL method).

Let's multiply (7 + 5i) and (8 - 6i):

```
(7 + 5i)(8 - 6i) = 7(8) + 7(-6i) + 5i(8) + 5i(-6i)
```

Simplify by performing the multiplication:

```
= 56 - 42i + 40i - 30i²
```

Remember that **i² = -1**. Substitute this value:

```
= 56 - 42i + 40i - 30(-1)
```

Combine real and imaginary terms:

```
= (56 + 30) + (-42 + 40)i
```

Finally, simplify:

```
= 86 - 2i
```

### Conclusion

Therefore, the product of (7 + 5i) and (8 - 6i) is **86 - 2i**.