Express (6+i )(2-i )/(4+3i )(1-2i) in the form a + ib
(6+i)(2−i)(4+3i)(1−2i)=12+2i−6i−i24+3i−8i−6i2=12+1−4i4+6−5i=13−4i10−5i=\frac{{(6 + i)(2 - i)}}{{\left( {4 + 3i} \right)\left( {1 - 2i} \right)}} = \frac{{12 + 2i - 6i - {i^2}}}{{4 + 3i - 8i - 6{i^2}}} = \frac{{12 + 1 - 4i}}{{4 + 6 - 5i}} = \frac{{13 - 4i}}{{10 - 5i}}=(4+3i)(1−2i)(6+i)(2−i)=4+3i−8i−6i212+2i−6i−i2=4+6−5i12+1−4i=10−5i13−4i=
=(13−4i)(10+5i)(10−5i)(10+5i)=130−40i+65i−20i2100+25=130+20125+25125i=65+15i= \frac{{(13 - 4i)(10 + 5i)}}{{(10 - 5i)(10 + 5i)}} = \frac{{130 - 40i + 65i - 20{i^2}}}{{100 + 25}} = \frac{{130 + 20}}{{125}} + \frac{{25}}{{125}}i = \frac{6}{5} + \frac{1}{5}i=(10−5i)(10+5i)(13−4i)(10+5i)=100+25130−40i+65i−20i2=125130+20+12525i=56+51i
Answer: 65+15i\frac{6}{5} + \frac{1}{5}i56+51i
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