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

5 answers

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:

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

I think the answer would be more simple then that

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!

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

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!