Question

Question Use the properties of complex number to simply (−49−−−−√+5i) +(8−−4−−−√) .(1 point) Responses 8+5i+−53−−−−√ 8 plus 5 i plus square root of negative 53 13+9i 13 plus 9 i 8+14i 8 plus 14 i 8+10i

Answer 1

nOT EVEN CLOSE TO THE OPTIONS PRESENTED

Answer 2

Use the properties of complex number to simplify the square root of -49 +5i + 8-square root of -4
A 8+5i+square root of -53
B 13+9i
8+14i
8+10i
I wrote this by hand it is all correct

Answer 3

To simplify the expression \((-49^{1/2} + 5i) + (8 - 4^{1/2})\), we need to handle each part separately.

1. Simplifying \(-49^{1/2}\):
\[
-49^{1/2} = -\sqrt{49} = -7
\]

2. The expression now is:
\[
(-7 + 5i) + (8 - 4^{1/2})
\]

3. Simplifying \(-4^{1/2}\):
\[
-4^{1/2} = -\sqrt{4} = -2
\]

4. So the expression becomes:
\[
(-7 + 5i) + (8 - 2)
\]

5. Simplifying the real parts:
\[
-7 + 8 - 2 = -1
\]

6. The expression now looks like:
\[
-1 + 5i
\]

Combining everything, we have:
\[
-1 + 5i
\]

This is not in the options provided. However, looking back at the interpretations of the expression \((−\sqrt{49}+5i) +(8-\sqrt{4})\) should lead us to the proper simplification:

7. Recall:
\[
-\sqrt{49} + 5i = -7 + 5i
\]
\[
8 - \sqrt{4} = 8 - 2 = 6
\]

Now adding the real parts correctly:
\[
-7 + 6 + 5i = -1 + 5i
\]

Since the provided form already mishandled by mixing signs, we find the correct interpretation aligned with our calculations does not exist in the options either. It should simply lead us to resolve \(-1 + 5i\).

If we wish to check further against the options, likely we'd be looking for something adaptable within bounds of what's near in context highlighting may yield a proper match, yet without redefining from original cues on roots would stray into misalignment.

In final recap, our core computation leads simply to:
\[
\boxed{-1 + 5i}
\]

If there are further matters regarding presented options to intertwine, please advise for refinements.

Answer 4

I apologize for the confusion in my previous response. Let's carefully reevaluate the expression step by step.

We're looking at the expression:

\[
(-\sqrt{-49} + 5i) + (8 - \sqrt{-4})
\]

1. First, let's rewrite \(-\sqrt{-49}\) using the imaginary unit \(i\):
\[
-\sqrt{-49} = -\sqrt{49}\cdot i = -7i
\]

2. Next, handle \(-\sqrt{-4}\):
\[
-\sqrt{-4} = -\sqrt{4}\cdot i = -2i
\]

Now, substituting these in, we have:

\[
(-7i + 5i) + (8 - 2i)
\]

3. Combine the imaginary parts:
\[
-7i + 5i = -2i
\]

So now we can add it all together:

\[
(8) + (-2i) = 8 - 2i
\]

This actually was looking off in prior, but tracking thus presently leads:

We have:
\[
8 - 2i
\]

Now looking at choices more closely made from:
- \(8 + 5i + \sqrt{-53}\)
- \(13 + 9i\)
- \(8 + 14i\)
- \(8 + 10i\)

We further need clearer framing from initial options being driven from:

Thus results were attained not lining with immediate segments. Please confirm if production was strictly right-to-write or miscalculated somewhere internally based on factors altering or adjusting signs along way through interpretations.

If looking for a tighter wrap or resolution across options, please reaffirm directive you seek on the quarter ahead or my computations. Thank you for your patience as we mirror through evaluations.

Answer 5

Let's go through the expression step by step:

The expression given is:

\[
\sqrt{-49} + 5i + 8 - \sqrt{-4}
\]

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

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

3. **Substitute these results back into the expression**:

Now we substitute back into the expression:

\[
7i + 5i + 8 - 2i
\]

4. **Combine the imaginary parts**:

Combine the imaginary parts:

\[
(7i + 5i - 2i) = 10i
\]

5. **Combine with the real part**:

Now, putting everything together:

\[
8 + 10i
\]

Now, looking at the options provided:
- A) \(8 + 5i + \sqrt{-53}\)
- B) \(13 + 9i\)
- C) \(8 + 14i\)
- D) \(8 + 10i\)

The simplified result is:

\[
\boxed{8 + 10i}
\]

Thus, the correct choice is **D)** \(8 + 10i\). Thank you for your patience!