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

This article will guide you through multiplying the complex numbers (7-3i) and (8+4i).

### 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 (i.e., i² = -1).

### Multiplication Process

To multiply complex numbers, we use the distributive property (also known as FOIL - First, Outer, Inner, Last):

**Multiply the First terms:**7 * 8 = 56**Multiply the Outer terms:**7 * 4i = 28i**Multiply the Inner terms:**-3i * 8 = -24i**Multiply the Last terms:**-3i * 4i = -12i²

### Simplifying the Result

Now, we have: 56 + 28i - 24i - 12i²

Since i² = -1, we can substitute: 56 + 28i - 24i - 12(-1)

Combining the real and imaginary terms: 56 + 12 + 28i - 24i = 68 + 4i

### Final Answer

Therefore, the product of (7-3i) and (8+4i) is **68 + 4i**.