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this is a very good question. lets solve (2+3i)/(4-2i).
we want to make 4-2i real by multiplying it by the conjugate, or 4+2i
(4-2i)(4+2i)=16-8i+8i+4=20, now we have
(2+3i)/20 0r 1/10 + 3i/20
notice that -2i times 2i = -4i^2 =-4 times -1 = 4
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