**Solving the Equation:**

Given the equation:

**(1 + 0) + (0 + 1) = A** and **(3i + 4a) (3i - 4a) = x^2i**

We are asked to find the value(s) of x.

**Step 1: Simplify the first equation**

The first equation can be simplified as:

**2 = A**

So, the value of A is 2.

**Step 2: Expand the second equation**

Using the distributive property, we can expand the second equation as:

**(3i + 4a) (3i - 4a) = 9i^2 - 16a^2 = x^2i**

**Step 3: Equate the imaginary and real parts**

Since the equation is equal to x^2i, we can equate the imaginary and real parts separately.

- Imaginary part:
**9i^2 = x^2i** - Real part:
**-16a^2 = 0**

**Step 4: Solve for x**

From the imaginary part, we can see that:

**9i^2 = x^2i**

Since i^2 = -1, we can rewrite the equation as:

**-9 = x^2**

Taking the square root of both sides, we get:

**x = ±√9 = ±3**

**Answer:**

Therefore, the value(s) of x are **x = 3** or **x = -3**.