To perform division in complex numbers, we multiply both the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of $1+2i$ is $1-2i$. Multiplying: \begin{align*}
\frac{-3+4i}{1+2i}&=\frac{(-3+4i)(1-2i)}{(1+2i)(1-2i)}\\
&=\frac{-3+4i+6i-8i^2}{1+2i-2i-4i^2}\\
&=\frac{5+10i}{5}\\
&=\boxed{1+2i}
\end{align*}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
William Sydney Porter tried to perform the calculation $\frac{-3+4i}{1+2i}$. However, he accidentally missed the minus sign, finding $\frac{3+4i}{1+2i}=\frac{11}{5}-\frac{2}{5}i$. What answer should he have obtained?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1+2i
William Sydney Porter tried to perform the calculation $\frac{-3+4i}{1+2i}$. However, he accidentally missed the minus sign, finding $\frac{3+4i}{1+2i}=\frac{11}{5}-\frac{2}{5}i$. What answer should he have obtained?
test