## Multiplying Complex Numbers: (7-6i)(-8+3i)

This article will guide you through the process of multiplying the complex numbers (7-6i) and (-8+3i).

### 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).

### Multiplying Complex Numbers

Multiplying complex numbers is similar to multiplying binomials. We use the distributive property (also known as FOIL - First, Outer, Inner, Last).

Let's multiply (7-6i) and (-8+3i):

**(7-6i)(-8+3i)** = 7(-8) + 7(3i) - 6i(-8) - 6i(3i)

Expanding the terms:

= -56 + 21i + 48i - 18i²

Remember that i² = -1. Substitute this into the equation:

= -56 + 21i + 48i - 18(-1)

Combining like terms:

= -56 + 18 + 21i + 48i

= **-38 + 69i**

### Final Result

Therefore, the product of (7-6i) and (-8+3i) is **-38 + 69i**.