Question

mplify the expression to a + bi form:
(-2 + 7i) - (-11 - 4i)

Explanation:

Step1: Distribute the negative sign

To simplify \((-2 + 7i) - (-11 - 4i)\), we first distribute the negative sign to the terms inside the second parentheses. This gives us \(-2 + 7i + 11 + 4i\) (because subtracting a negative is like adding a positive, so \(-(-11)=11\) and \(-(-4i)=4i\)).

Step2: Combine the real parts and the imaginary parts

Now, we combine the real parts (\(-2\) and \(11\)) and the imaginary parts (\(7i\) and \(4i\)) separately.
For the real parts: \(-2 + 11 = 9\)
For the imaginary parts: \(7i + 4i = 11i\)
Putting these together, we get the expression in \(a + bi\) form.

Answer:

\(9 + 11i\)