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# complex numbers

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Simplify $\dfrac{5+12i}{2-8i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).

Feb 21, 2021

$$\frac{5+12i}{2-8i} \cdot \frac{2+8i}{2+8i} = \frac{10+24i+40i+96i^2}{70} = \boxed{\frac{-43+32i}{35}}$$