Simplify (9+ star rt -4) + (-9 - sqr rt -16)

1 answer

To simplify the expression \((9 + \sqrt{-4}) + (-9 - \sqrt{-16})\), we can start by simplifying each part.

First, let's simplify \(\sqrt{-4}\): \[ \sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i \]

Now, we simplify \(\sqrt{-16}\): \[ \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i \]

Now we can substitute these values back into the expression:

\[ (9 + 2i) + (-9 - 4i) \]

Now, combine the real parts and the imaginary parts:

For the real parts: \[ 9 + (-9) = 0 \]

For the imaginary parts: \[ 2i + (-4i) = 2i - 4i = -2i \]

Thus, the simplified expression is: \[ 0 - 2i = -2i \]

So, the final answer is: \[ \boxed{-2i} \]