The solutions to the given equation are:

$z_1 = -\frac{1}{2} + \frac{5i}{2}$ $z_2 = \frac{4}{17} + \frac{35i}{17}$

Would you like further details on the solution process?

Here are 5 related questions to explore further:

1. How would you solve a similar equation with different complex numbers?
2. What is the significance of complex roots in equations like this one?
3. Can you graph these complex solutions on the complex plane?
4. How does changing the coefficients in the equation affect the solutions?
5. What are the geometric interpretations of the transformations in complex numbers?

Tip: When solving equations involving complex numbers, always check if the denominator introduces any constraints (e.g., division by zero).