Question

simplify.
-(8i - 3) + (-10 + 10i)
write your answer in the form a + bi.

Explanation:

Step1: Distribute the negative sign

First, we distribute the negative sign in \(-(8i - 3)\). This gives us \(-8i + 3\) (because \(-(a - b)=-a + b\), so here \(a = 8i\) and \(b = 3\), so \(-(8i - 3)=-8i+3\)).

Step2: Combine with the second complex number

Now we have \(-8i + 3+(-10 + 10i)\). We combine the real parts and the imaginary parts separately. The real parts are \(3\) and \(-10\), and the imaginary parts are \(-8i\) and \(10i\).
For the real parts: \(3+(-10)=3 - 10=-7\).
For the imaginary parts: \(-8i+10i = 2i\).

Step3: Write in \(a + bi\) form

Combining the real and imaginary parts, we get \(-7+2i\).

Answer:

\(-7 + 2i\)