Let's solve the given expression step by step:

$(3.4 + \sqrt{-25}) - (-9 - \sqrt{-9})$

Step 1: Express Square Roots of Negative Numbers Using $i$

• $\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i$
• $\sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i$

Now, rewriting the given expression:

$(3.4 + 5i) - (-9 - 3i)$

Step 2: Distribute the Negative Sign

$3.4 + 5i + 9 + 3i$

Step 3: Combine Like Terms

• Real part: $3.4 + 9 = 12.4$
• Imaginary part: $5i + 3i = 8i$

Final Answer:

$\mathbf{12.4 + 8i}$

Let me know if you want further clarification!

Related Questions:

1. How do you simplify expressions involving imaginary numbers?
2. What is the significance of the imaginary unit $i$?
3. How do you add and subtract complex numbers?
4. Can complex numbers be graphed on a coordinate plane?
5. How do you multiply and divide complex numbers?

Tip: Always remember that $i^2 = -1$ when working with imaginary numbers!