(−3−i)⋅(3+i)

Jasonbradley

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Jun 17, 2024

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Multiplying Complex Numbers: (-3 - i) * (3 + i)

This article will demonstrate how to multiply two complex numbers, specifically (-3 - i) * (3 + i).

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).

Multiplication Process

To multiply complex numbers, we follow a similar process to multiplying binomials:

1. Distribute: Multiply each term in the first complex number by each term in the second complex number.
2. Simplify: Combine like terms, remembering that i² = -1.

Applying the Process

Let's multiply (-3 - i) * (3 + i):

1. Distribute:

   • -3 * 3 = -9
   • -3 * i = -3i
   • -i * 3 = -3i
   • -i * i = -i²

2. Simplify:

   • -9 - 3i - 3i - i²
   • -9 - 6i - (-1) (Since i² = -1)
   • -9 + 1 - 6i
   • -8 - 6i

Result

Therefore, the product of (-3 - i) * (3 + i) is -8 - 6i.