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Complex Number Arithmetic

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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?

Feb 21, 2021

$$\frac{-3+4i}{1+2i} \cdot \frac{1-2i}{1-2i} = \frac{-3+4i+6i-8i^2}{5} = \boxed{\frac{11+10i}{5}}$$