We are given a system of complex linear equations for part (a):

$(3 - i)x + (4 + 2i)y = 2 + 6i$ $(4 + 2i)x - (2 + 3i)y = -5 + 4i$

We can solve this system step by step using substitution or elimination. First, let's express the system of equations clearly.

Step 1: Write the equations

1. $(3 - i)x + (4 + 2i)y = 2 + 6i$
2. $(4 + 2i)x - (2 + 3i)y = -5 + 4i$

We can solve this using matrix or substitution methods. Let's use elimination.

Step 2: Eliminate one variable

We multiply the first equation by the coefficient of $x$ in the second equation, and the second equation by the coefficient of $x$ in the first equation, and subtract.

Let me compute this.The solution to the system of complex equations is:

$x = \frac{-33}{97} + \frac{147i}{97}$ $y = \frac{40}{97} + \frac{7i}{97}$

If you need further details or a breakdown of the steps, feel free to ask!

Here are 5 related questions you can explore next:

1. How would the method change if all coefficients were real numbers?
2. Can we represent the solution in polar form instead of rectangular?
3. How does Gaussian elimination work with complex numbers?
4. What are some applications of complex systems of equations in engineering?
5. Can this system be solved graphically in the complex plane?

Tip: When dealing with complex numbers, remember to treat the real and imaginary parts separately when performing arithmetic operations.