Subtract (2.5+−36−−−−√)−(7−−4−−−√)

Question

(
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: \[ \boxed{(2.5 - \sqrt{7}) + 8i} \]