Question

Use the properties of complex numbers to simplify (sqrt(-49)+5i)+(8-sqrt(-4)). (1 point) 13+9i 8+5i+sqrt(-53) 8+10i 8+14i

Answer 1

To simplify the expression \((\sqrt{-49}+5i)+(8-\sqrt{-4})\), we first compute the individual terms involving the square roots of negative numbers.

1. **Calculate \(\sqrt{-49}\)**:
\[
\sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i
\]

2. **Calculate \(\sqrt{-4}\)**:
\[
\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i
\]

Now we can rewrite the expression using these results:
\[
(7i + 5i) + (8 - 2i)
\]

3. **Combine the imaginary parts**:
\[
7i + 5i = 12i
\]

So we have:
\[
12i + (8 - 2i) = 8 + 12i - 2i = 8 + 10i
\]

Now, we can summarize the simplified expression:
\[
\text{Final Result: } 8 + 10i
\]

Therefore, the simplified form of the expression is:
\[
\boxed{8 + 10i}
\]