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:
- Distribute: Multiply each term in the first complex number by each term in the second complex number.
- Simplify: Combine like terms, remembering that i² = -1.
Applying the Process
Let's multiply (-3 - i) * (3 + i):
-
Distribute:
- -3 * 3 = -9
- -3 * i = -3i
- -i * 3 = -3i
- -i * i = -i²
-
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.