(-3+2i)(-6-8i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (-3 + 2i)(-6 - 8i)

This article will guide you through the process of multiplying two complex numbers: (-3 + 2i) and (-6 - 8i).

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 (i.e., i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property (also known as FOIL method):

1. Multiply the first terms: (-3) * (-6) = 18
2. Multiply the outer terms: (-3) * (-8i) = 24i
3. Multiply the inner terms: (2i) * (-6) = -12i
4. Multiply the last terms: (2i) * (-8i) = -16i²

Now, we have: 18 + 24i - 12i - 16i²

Remember that i² = -1. Substituting this:

18 + 24i - 12i - 16(-1)

Simplifying the expression:

18 + 24i - 12i + 16

Combining real and imaginary terms:

(18 + 16) + (24 - 12)i

Result

Therefore, the product of (-3 + 2i) and (-6 - 8i) is: 34 + 12i