Question

subtract (2.5+−36−−−−√)−(7−−4−−−√) . Provide your answer in the form of a+bi Note: Enter your answer and SHOW ALL THE STEPS NECESSARY to solve this problem in the space provided. You will not receive credit without all work shown. (You may use the image icon to upload your work)

Answer 1

To solve the expression \( (2.5 + \sqrt{-36}) - \sqrt{7} \), we first need to simplify each term.

### Step 1: Simplify \( \sqrt{-36} \)
Since \(-36\) is negative, we need to express it in terms of imaginary numbers:

\[
\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i
\]

### Step 2: Rewrite the Expression
Now we substitute the simplified form of \( \sqrt{-36} \) into the expression:

\[
(2.5 + 6i) - \sqrt{7}
\]

### Step 3: Simplifying Further
Since \( \sqrt{7} \) is a real number, we will simply subtract \( \sqrt{7} \) from the real part \( 2.5 \):

\[
2.5 - \sqrt{7} + 6i
\]

### Step 4: Final Form
Now we have our expression in the form \( a + bi \). Here, \( a = 2.5 - \sqrt{7} \) and \( b = 6 \).

Thus, the final answer is:

\[
(2.5 - \sqrt{7}) + 6i
\]

### Summary
The simplified form of the expression \( (2.5 + \sqrt{-36}) - \sqrt{7} \) is

\[
(2.5 - \sqrt{7}) + 6i
\]

This is your final answer.