The given mathematical expression is:

$(9i^2 + 14i - 5) + (9i^2 - 11i + 4)$

Step-by-step Solution:

1. Simplify $i^2$: Recall that $i^2 = -1$.

   Substitute $i^2 = -1$ into the expression: $(9(-1) + 14i - 5) + (9(-1) - 11i + 4)$

2. Simplify each part:

   • First term: $9(-1) + 14i - 5 = -9 + 14i - 5 = -14 + 14i$
   • Second term: $9(-1) - 11i + 4 = -9 - 11i + 4 = -5 - 11i$

3. Combine the two terms: Add $(-14 + 14i)$ and $(-5 - 11i)$: $(-14 + 14i) + (-5 - 11i) = (-14 - 5) + (14i - 11i)$ Simplify: $-19 + 3i$

Final Answer:

$-19 + 3i$

Would you like further details on this or explanations about $i^2$ and complex numbers?

Here are some related questions to deepen your understanding:

1. What is the geometric representation of $i$ on the complex plane?
2. How is addition of complex numbers visualized graphically?
3. What happens when you multiply two imaginary numbers like $i \cdot i$?
4. What are the polar forms of complex numbers, and how do they relate to Cartesian form?
5. Can you identify the modulus and argument of a complex number like $-19 + 3i$?

Tip: Always simplify powers of $i$ by remembering the pattern $i^2 = -1, i^3 = -i, i^4 = 1$, and so on!