## Multiplying Complex Numbers: (7+3i)(-7+5i)(-8-4i)

This article will guide you through multiplying three complex numbers: (7+3i)(-7+5i)(-8-4i). We will break down the process step by step to make it easier to follow.

### Step 1: Multiply the first two complex numbers

We start by multiplying the first two complex numbers: (7+3i)(-7+5i).

To do this, we use the distributive property (or FOIL method):

```
(7+3i)(-7+5i) = (7)(-7) + (7)(5i) + (3i)(-7) + (3i)(5i)
```

Simplifying:

```
= -49 + 35i - 21i + 15i²
```

Remember that *i² = -1*. Substituting this:

```
= -49 + 35i - 21i - 15
= -64 + 14i
```

### Step 2: Multiply the result by the third complex number

Now we have (-64 + 14i) and we need to multiply it by (-8-4i):

```
(-64 + 14i)(-8-4i) = (-64)(-8) + (-64)(-4i) + (14i)(-8) + (14i)(-4i)
```

Simplifying:

```
= 512 + 256i - 112i - 56i²
```

Again, substitute *i² = -1*:

```
= 512 + 256i - 112i + 56
= 568 + 144i
```

### Final Result

Therefore, the product of (7+3i)(-7+5i)(-8-4i) is **568 + 144i**.