It looks like you're working on complex numbers in the form of $a + bi$, and the answers for parts (a), (b), and (c) seem to have been partially evaluated.

Let’s go through them step by step to check what went wrong:

Part (a):
We are given $(1 + 4i)^2$.

First, we expand: $(1 + 4i)^2 = (1)^2 + 2(1)(4i) + (4i)^2$ $= 1 + 8i + 16i^2$ Since $i^2 = -1$, we get: $1 + 8i - 16 = -15 + 8i$ So, the correct answer for part (a) is $-15 + 8i$, which looks correct.

Part (b):
We are given $i(\pi - 4i)$.

Distribute the $i$: $i(\pi - 4i) = i\pi - 4i^2$ Since $i^2 = -1$, we get: $i\pi + 4 = 4 + i\pi$ So, the correct answer for part (b) is $4 + \pi i$, which also seems correct.

Part (c):
We are given $\frac{-3 + 5i}{i}$.

We can multiply both the numerator and the denominator by $i$ to simplify: $\frac{-3 + 5i}{i} \times \frac{i}{i} = \frac{(-3 + 5i)i}{i^2}$ Since $i^2 = -1$, this simplifies to: $\frac{-3i + 5i^2}{-1} = \frac{-3i - 5}{-1} = 3i + 5$ Thus, the correct answer for part (c) is $5 + 3i$, but your submission shows $-3i$, which is incorrect.

Would you like more detailed steps or help with anything else related to complex numbers?

Here are five related questions to deepen your understanding:

1. How do we handle the complex conjugate when dividing complex numbers?
2. What does it mean for a complex number to be in the form $a + bi$?
3. How do you simplify powers of $i$ (e.g., $i^3$, $i^4$)?
4. What is the geometric interpretation of multiplying two complex numbers?
5. How can you check if the real and imaginary parts of your complex number calculations are correct?

Tip: To avoid errors when expanding or simplifying complex numbers, remember to always check for $i^2 = -1$ in your steps!