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\frac{3+4 i}{2-7 i}=\frac{3+4 i}{2-7 i} \cdot \frac{2+7 i}{2+7 i}=\frac{6+21 i+8 i+28 i^{2}}{4+14 i-14 i-49 i^{2}}=\frac{-22+29 i}{4+49}=-\frac{22}{53}+\frac{29}{53} i