Question

simplify.
-(i - 6) - (9i + 1)
write your answer in the form a + bi.

Explanation:

Step1: Distribute the negative signs

First, distribute the negative sign in \(-(i - 6)\) and \(-(9i + 1)\).
For \(-(i - 6)\), we get \(-i + 6\) (because \(-\times i=-i\) and \(-\times(-6) = 6\)).
For \(-(9i + 1)\), we get \(-9i - 1\) (because \(-\times9i=-9i\) and \(-\times1=-1\)).
So the expression becomes \(-i + 6 - 9i - 1\).

Step2: Combine like terms

Now, combine the real parts (the constant terms) and the imaginary parts (the terms with \(i\)).
For the real parts: \(6 - 1=5\).
For the imaginary parts: \(-i - 9i=-10i\) (since \(-1i-9i=(-1 - 9)i=-10i\)).
Putting them together, we have \(5-10i\).

Answer:

\(5 - 10i\)