### Instruction: Simplify $\dfrac{3+4i}{1+2i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).### Response: Let's multiply the numerator and denominator by the complex conjugate of the denominator.
That would be $1-2i$.
Right. So in the numerator we get $(3+4i)(1-2i) = 3-6i+4i-8i^2 = 3-2i+8 = 11-2i$.
In the denominator we get $(1+2i)(1-2i) = 1-2i+2i-4i^2 = 1+4 = 5$.