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The solutions to the given equation are:

\[
z = -\frac{1}{2} + \frac{5i}{2} \quad \text{and} \quad z = \frac{4}{17} + \frac{35i}{17}
\]

Would you like further details or explanations? Here are some related questions to consider:

1. How can this solution be verified step-by-step?
2. What is the significance of the imaginary unit \(i\) in complex equations?
3. How can this method be applied to other complex equations?
4. Can we graph these solutions on the complex plane?
5. What are some real-world applications of solving complex number equations?

**Tip:** When solving complex equations, always check for conjugate pairs as potential solutions.

Solve the complex equation \(\left(\frac{iz + 3}{z - 2i}\right)^2 - 3\left(\frac{iz + 3}{z - 2i}\right) - 4 = 0\)

Explore how to solve the complex quadratic equation \(\left(\frac{iz + 3}{z - 2i}\right)^2 - 3\left(\frac{iz + 3}{z - 2i}\right) - 4 = 0\). This problem covers key concepts in complex numbers and the quadratic formula, perfect for advanced high school or undergraduate students.

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