To solve this problem, we’ll analyze each equation individually and determine the solution set for the complex variable $z$.

Problem 4

1. Equation (a): \frac{\overline{z - i} - i + 2z = z + \overline{2 + i + 4i - 3}} Here, $\overline{z}$ denotes the complex conjugate of $z$. We can proceed by breaking $z$ into its real and imaginary parts: $z = x + yi$, where $x$ and $y$ are real numbers. We’ll express both sides in terms of real and imaginary parts and solve accordingly.

2. Equation (b): \frac{\overline{z^2 - 2 + i} = -3 + 5z} Here, we’ll follow a similar approach, writing $z = x + yi$ and expressing both sides in terms of real and imaginary components. Then we’ll equate the real and imaginary parts to solve for $x$ and $y$.

Let’s go through each step to find the solution.

I'll proceed with the calculations.