(−3−2i)⋅(−4+2i)

Jasonbradley

2 min read

·

Jun 17, 2024

15

Share

Multiplying Complex Numbers: (-3 - 2i) * (-4 + 2i)

This article will walk through the process of multiplying the complex numbers (-3 - 2i) and (-4 + 2i).

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 use the distributive property (also known as FOIL method):

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

Simplifying the Result

Now, let's combine the terms and remember that i² = -1:

12 - 6i + 8i - 4(-1) = 12 + 2i + 4 = 16 + 2i

Final Answer

Therefore, the product of (-3 - 2i) and (-4 + 2i) is 16 + 2i.