Question

find the sum or difference.
$-i\sqrt{3} - 4 - (4 - 6i\sqrt{3}) - (2 - i\sqrt{3})$
$-i\sqrt{3} - 4 - (4 - 6i\sqrt{3}) - (2 - i\sqrt{3}) = \square$
(simplify your answer. type your answer in the form $a + bi$. type an exact

Explanation:

Step1: Remove parentheses

To remove the parentheses, we distribute the negative signs:
\[

$$\begin{align*} &-i\sqrt{3}-4-(4 - 6i\sqrt{3})-(2 - i\sqrt{3})\\ =&-i\sqrt{3}-4 - 4+6i\sqrt{3}-2 + i\sqrt{3} \end{align*}$$

\]

Step2: Combine real parts

The real parts are \(-4\), \(-4\), and \(-2\). Combine them:
\[
-4-4 - 2=-10
\]

Step3: Combine imaginary parts

The imaginary parts are \(-i\sqrt{3}\), \(6i\sqrt{3}\), and \(i\sqrt{3}\). Combine them:
\[
(-1 + 6+1)i\sqrt{3}=6i\sqrt{3}
\]

Step4: Combine real and imaginary parts

Combine the results from Step 2 and Step 3:
\[
-10 + 6i\sqrt{3}
\]

Answer:

\(-10 + 6i\sqrt{3}\)