The image you've uploaded contains various mathematical problems involving complex functions. Let's break it down by sections:

1. Operations with Complex Numbers:

   • (a) Compute $\frac{2 + 3i}{3 - 2i}$
   • (b) Compute $\frac{1 + i}{1 - i}$

2. Solve the equation and verify the solution:

   • Solve the quadratic equation: $x^2 - 2x + 2 = 0$.

3. Represent on the complex plane:

   • Represent $z = 5$ and $z = 1 - i$ on the complex plane, both in trigonometric and exponential form.

4. Differentiation:

   • If the function is differentiable, find its derivative: $f(z) = (x^3 - 3xy^2) + i(3x^2y - y^3)$.

5. Find the original function:

   • Find the original function given its derivative $f'(p) = \frac{1}{p(p - 1)}$.

6. Solve the differential equation with initial conditions:

   • Solve the differential equation $y'' - 2y' = e^{x}$, with initial conditions $y(0) = -1$ and $y'(0) = 0$.

Would you like me to start solving each of these one by one, or do you have a specific question you'd like to begin with?