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

This article will guide you through the process of multiplying complex numbers and expressing the result in standard form (a + bi).

### 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

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

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

### Simplifying the Expression

Now, let's simplify the expression:

**56 - 42i + 40i - 30i²**

Remember that **i² = -1**, so we can substitute:

**56 - 42i + 40i + 30**

### Combining Real and Imaginary Terms

Finally, combine the real terms and the imaginary terms:

**(56 + 30) + (-42 + 40)i**

### Standard Form

The simplified expression in standard form is:

**86 - 2i**

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