Question

Subtract (2.5+−36−−−−√)−(7−−4−−−√)
(
2.5
+
−
36
)
−
(
7
−
−
4
)
. Provide your answer in the form of a+bi
𝑎
+
𝑏
𝑖



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.

Answer 1

To solve the expression \((2.5 + \sqrt{-36}) - (\sqrt{7} - \sqrt{-4})\), we need to simplify each part step by step.

### Step 1: Simplify \(\sqrt{-36}\)

The square root of a negative number can be expressed using the imaginary unit \(i\).
\[
\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i
\]

### Step 2: Simplify \(\sqrt{-4}\)

Similarly, we simplify \(\sqrt{-4}\):
\[
\sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i
\]

### Step 3: Rewrite the expression using these simplifications

Now we can rewrite the original expression:
\[
(2.5 + 6i) - (\sqrt{7} - 2i)
\]

### Step 4: Distribute the negative sign through

Next, we distribute the negative sign in the second part:
\[
(2.5 + 6i) - \sqrt{7} + 2i
\]
This gives us:
\[
2.5 - \sqrt{7} + 6i + 2i
\]

### Step 5: Combine like terms

Now we combine the real parts and the imaginary parts:
- Real part: \(2.5 - \sqrt{7}\)
- Imaginary part: \(6i + 2i = 8i\)

### Final Result

Putting it all together, we get:
\[
(2.5 - \sqrt{7}) + 8i
\]

Thus, the final result in the form \(a + bi\) is:
\[
\boxed{(2.5 - \sqrt{7}) + 8i}
\]