Question

simplify the expression to a + bi form: (-5 - 4i) - (7 + 8i)

Explanation:

Step1: Distribute the negative sign

To simplify \((-5 - 4i) - (7 + 8i)\), we first distribute the negative sign to the terms inside the second parentheses. This gives us \(-5 - 4i - 7 - 8i\).

Step2: Combine the real parts and the imaginary parts

Next, we combine the real parts (\(-5\) and \(-7\)) and the imaginary parts (\(-4i\) and \(-8i\)) separately.
For the real parts: \(-5 - 7 = -12\)
For the imaginary parts: \(-4i - 8i = -12i\)
Putting these together, we get the simplified form.

Answer:

\(-12 - 12i\)