(-2-7i)(-12+6i)

Jasonbradley

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Jun 16, 2024

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Multiplying Complex Numbers: (-2 - 7i)(-12 + 6i)

This article will guide you through the process of multiplying two complex numbers: (-2 - 7i) and (-12 + 6i).

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 (also known as FOIL method):

1. Multiply the first terms: (-2) * (-12) = 24
2. Multiply the outer terms: (-2) * (6i) = -12i
3. Multiply the inner terms: (-7i) * (-12) = 84i
4. Multiply the last terms: (-7i) * (6i) = -42i²

Now we have: 24 - 12i + 84i - 42i²

Since i² = -1, we can substitute it:

24 - 12i + 84i - 42(-1)

Simplifying the expression:

24 - 12i + 84i + 42

Combining the real and imaginary terms:

(24 + 42) + (-12 + 84)i

The Final Result

Therefore, the product of (-2 - 7i) and (-12 + 6i) is 66 + 72i.