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: $$\boxed{{\displaystyle (2.5-\sqrt{7})+8i}}$$