(6-8i)(9+2i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (6-8i)(9+2i)

This article will walk through the process of multiplying two complex numbers, (6-8i) and (9+2i).

Understanding Complex Numbers

Complex numbers are numbers of 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).

Multiplication Process

To multiply complex numbers, we use the distributive property, similar to multiplying binomials:

(6-8i)(9+2i) = 6(9) + 6(2i) - 8i(9) - 8i(2i)

Simplifying the Expression

Let's simplify the expression step by step:

1. Multiply the terms:

   • 6(9) = 54
   • 6(2i) = 12i
   • -8i(9) = -72i
   • -8i(2i) = -16i²

2. Substitute i² with -1:

   • -16i² = -16(-1) = 16

3. Combine like terms:

   • 54 + 12i - 72i + 16 = 70 - 60i

Final Result

Therefore, the product of (6-8i) and (9+2i) is 70 - 60i.