First, let's reshape the equation so that only x remains on one side. To achieve this, we subtract the term (13 - 41) from both sides of the equation. This gives us:
(2 + 3i)x = (10 + 8i) - (13 - 41)
Simplify the right-hand side of the equation:
(2 + 3i)x = 10 + 8i - 13 + 41
The result is:
(2 + 3i)x = -3 + 49i
The next step is to divide the equation by the coefficient for x, which is the complex number (2 + 3i). This will isolate x on one side of the equation. The new equation is:
x = (-3 + 49i) / (2 + 3i)
Performing this division operation gives us:
x = 7.692307692307692 - 7.538461538461538i
This is the solution to the equation in terms of the complex number x.