## Multiplying Complex Numbers: (8 + i)(2 + 7i)

This article will explore how to multiply the complex numbers (8 + i) and (2 + 7i).

### 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.

### The Multiplication Process

To multiply complex numbers, we use the distributive property (often referred to as FOIL for First, Outer, Inner, Last) just like we would with binomials.

**Step 1: Expand the product**

(8 + i)(2 + 7i) = (8 * 2) + (8 * 7i) + (i * 2) + (i * 7i)

**Step 2: Simplify**

= 16 + 56i + 2i + 7i²

**Step 3: Substitute i² with -1**

= 16 + 56i + 2i + 7(-1)

**Step 4: Combine real and imaginary terms**

= (16 - 7) + (56 + 2)i

**Step 5: Final result**

= **9 + 58i**

### Conclusion

Therefore, the product of the complex numbers (8 + i) and (2 + 7i) is **9 + 58i**.