The problem asks us to add two complex numbers: $(3 + i\sqrt{2})$ and $(-4 + i\sqrt{2})$.

1. Problem Description

The problem asks us to add two complex numbers: $(3 + i\sqrt{2})$ and $(-4 + i\sqrt{2})$.

2. Solution Steps

To add two complex numbers, we add their real parts and their imaginary parts separately.

Let $z_1 = a + bi$ and $z_2 = c + di$ be two complex numbers, where $a, b, c, d$ are real numbers and $i$ is the imaginary unit ($i^2 = -1$).

Then, $z_1 + z_2 = (a+c) + (b+d)i$.

In our case, $z_1 = 3 + i\sqrt{2}$ and $z_2 = -4 + i\sqrt{2}$. So, $a = 3$, $b = \sqrt{2}$, $c = -4$, and $d = \sqrt{2}$.

Therefore,

$z_1 + z_2 = (3 + (-4)) + (\sqrt{2} + \sqrt{2})i = (3 - 4) + (2\sqrt{2})i = -1 + 2\sqrt{2}i$.

3. Final Answer

The sum of the two complex numbers is $-1 + 2i\sqrt{2}$.