Express $(4-5i)(-5+5i)$ in the form $a+bi$, where $a$ and $b$ are integers and $i^2 = -1.$
To multiply two complex numbers, I can use the distributive property and combine like terms. I will also use the fact that $i^2 = -1$ to simplify any powers of $i$ that appear. So, I have $(4-5i)(-5+5i) = 4(-5) + 4(5i) - 5i(-5) - 5i(5i)$. This simplifies to $-20 + 20i + 25i - 25i^2$. Now, I can replace $i^2$ with $-1$ and get $-20 + 20i + 25i + 25$. Finally, I can combine the real and imaginary parts and write the answer in the form $a+bi$. The answer is $5 + 45i$. 