((2+i)/(3-i))+((2-i)/(4i)) explanation please

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((2+i)/(3-i))+((2-i)/(4i)) explanation please

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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do u know that these are complex numbers eg 2 + i
yes
u need to rationalise the denominators by multiplying them by their complements the complement of 3-i is 3+i (changed sign) so we have (2+i)((3+i)/(3-i)(3+i) + (2-i)4i / 4i(4i) (6+2i+3i -1)/ 9+1 + 8i +4/-16 (5 +5i )/ 10 - (8i+4)16

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what do i do after that?
i suppose we should write it as one fraction (1+i) / 2 - (2i+1) / 4 = (2+2i )/ 4 - (2i+1) / 4 = 1/4
do i need a common denominator?
wow - that neat- if i'm right of couse
you are i checked it on my calculator but i didnt know how to get it.... and i factor right?
sorry i dont know exactly what you mean (i'm a brit see!!)
nevermind but thanks
i understand it now
good

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