Simplify the following product of complex numbers. (8 + i) • (-4 – 3i)
use good-old-fashioned FOIL
= -32 _ 24i - 4i - 3i^2
= -32 - 28i + 3
= -29 - 28i
(x^2 + 3) ^2
To simplify the product of complex numbers (8 + i) • (-4 - 3i), we can use the distributive property and the rules of complex number multiplication.
First, we distribute the real terms and the imaginary terms separately:
8 • (-4 - 3i) + i • (-4 - 3i)
Next, we multiply each term within the parentheses:
-32 - 24i + (-4i) - 3i^2
Now, we simplify the expression by combining like terms and using the fact that i^2 equals -1:
-32 - 24i - 4i + 3
Finally, we combine the real terms and imaginary terms:
-29 - 28i
So, the simplified product of (8 + i) • (-4 - 3i) is -29 - 28i.