Question

Evaluate the subtraction (13+√-225)−(49√-2i) . Provide the answer in the form a+bi .(1 point)

Answer 1

I think the answer would be more simple then that

Answer 2

Well its a blank box not mutiple choice so I just thought it would be a little simpler

Answer 3

To evaluate the expression \((13 + \sqrt{-225}) - (49\sqrt{-2}i)\), we will first simplify each component.

1. **Simplify \(\sqrt{-225}\)**:
\[
\sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i
\]

2. **Simplify \(49\sqrt{-2}\)**:
\[
\sqrt{-2} = \sqrt{2} \cdot \sqrt{-1} = \sqrt{2}i
\]
Thus,
\[
49\sqrt{-2} = 49\sqrt{2}i
\]

Now substitute these values into the original expression:

\[
(13 + 15i) - (49\sqrt{2}i)
\]

Combine the imaginary parts:

\[
= 13 + (15i - 49\sqrt{2}i)
\]
\[
= 13 + (15 - 49\sqrt{2})i
\]

Final result in the form \(a + bi\):

\[
= 13 + (15 - 49\sqrt{2})i
\]

So, the answer is:

\[
\boxed{13 + (15 - 49\sqrt{2})i}
\]

Answer 4

Let's re-evaluate the expression step-by-step more clearly and simplify it further.

Given the expression:

\[
(13 + \sqrt{-225}) - (49\sqrt{-2}i)
\]

### Step 1: Simplify \(\sqrt{-225}\)

\[
\sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i
\]

### Step 2: Simplify \(49\sqrt{-2}\)

The term \(49\sqrt{-2}\) has a complex component. First, we simplify it:

\[
\sqrt{-2} = \sqrt{2} \cdot \sqrt{-1} = \sqrt{2}i
\]

So,

\[
49\sqrt{-2} = 49\sqrt{2}i
\]

### Step 3: Substitute Back into the Expression

Now substitute these simplified components back into the expression:

\[
(13 + 15i) - (49\sqrt{2}i)
\]

### Step 4: Combine Like Terms

Now, combine the imaginary parts:

\[
= 13 + (15i - 49\sqrt{2}i)
\]

\[
= 13 + (15 - 49\sqrt{2})i
\]

### Final Answer

The final simplified expression, clearly stated in the form \(a + bi\), remains:

\[
\boxed{13 + (15 - 49\sqrt{2})i}
\]

This result cannot be simplified further into a simpler form given that \(49\sqrt{2}\) is a numeric constant. Let me know if you were looking for a numerical approximation or had a different interpretation in mind!

Answer 5

Let's simplify the calculation once more to ensure the result is in the simplest possible form.

We need to evaluate:

\[
(13 + \sqrt{-225}) - (49\sqrt{-2}i)
\]

### Step 1: Calculate \(\sqrt{-225}\)

\[
\sqrt{-225} = 15i
\]

### Step 2: Calculate \(49\sqrt{-2}\)

\[
\sqrt{-2} = \sqrt{2}i \implies 49\sqrt{-2} = 49\sqrt{2}i
\]

### Step 3: Substitute Back Into the Expression

Now put all the parts back into the expression:

\[
(13 + 15i) - (49\sqrt{2}i)
\]

### Step 4: Combine Like Terms

Combine the imaginary components:

\[
= 13 + (15 - 49\sqrt{2})i
\]

So the result is:

\[
\text{Real part: } 13
\]
\[
\text{Imaginary part: } 15 - 49\sqrt{2}
\]

### Final Output

The expression in its simplest form remains:

\[
\boxed{13 + (15 - 49\sqrt{2})i}
\]

However, if you're looking for a numerical approximation to make it simpler:

### Simple Approximation

Calculating \(49\sqrt{2}\):

- \(\sqrt{2} \approx 1.414\)
- Thus, \(49\sqrt{2} \approx 49 \times 1.414 \approx 69.8\)

Now,

\[
15 - 49\sqrt{2} \approx 15 - 69.8 \approx -54.8
\]

So, the approximate result would be:

\[
\approx 13 - 54.8i
\]

Final simpler numerical form can be:

\[
\boxed{13 - 54.8i}
\]

Let me know if this meets your expectation!