Use the properties of complex numbers to simplify (−49−−−−√+5i)+(8−−4−−−√)

Question

(
−
49
+
5
𝑖
)
+
(
8
−
−
4
)
.(1 point)
Responses

8+5i+−53−−−−√
8
+
5
𝑖
+
−
53
8 plus 5 i plus square root of negative 53

8+10i
8
+
10
𝑖
8 plus 10 i

13+9i
13
+
9
𝑖
13 plus 9 i

8+14i

Answer 1

To simplify the expression \((-\sqrt{49} + 5i) + (8 - \sqrt{-4})\), we start by simplifying each part.

1. Simplify \(-\sqrt{49}\): \[ -\sqrt{49} = -7 \]

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

Now, substitute these values back into the expression: \[ (-7 + 5i) + (8 - 2i) \]

Next, combine the real parts and the imaginary parts:

• Real parts: \(-7 + 8 = 1\)
• Imaginary parts: \(5i - 2i = 3i\)

Thus, we have: \[ 1 + 3i \]

None of the options provided match the expression \(1 + 3i\). Therefore, let's double-check the simplification of \(\sqrt{-4}\):

• \(\sqrt{-4}\) should contribute as \(-2i\) when we write it as \(-\sqrt{-4}\).

Let's redo the imaginary parts:

• Real parts: \(-7 + 8 = 1\)
• Imaginary parts: \(5i - 2i = 3i\)

So the expression should simplify to: \[ 1 + 3i \] After reviewing all steps, it appears that the simplified answer is \(1 + 3i\) which also doesn't match the given choices.

It seems there was a mistake in typing out the original expression or a misunderstanding in combining parts. If there are any clarifications or adjustments in the expression needed, please let me know!