(8+i)(2+7i)

Jasonbradley

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Jun 16, 2024

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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.