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" "(1+i)^(2)/(2-i)= x+ iy, "then fi...

`" "(1+i)^(2)/(2-i)= x+ iy, "then find the value of x+y"`.

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Given that , `" "(1+i)^(2)/(2-i)= x+ iy`
`rArr ((1+i^(2)+2))/(2-i)= x + iy rArr (2i)/(2-i) = x +iy`
`rArr (2i(2+i))/((2-i)(2+i))= x + iy rArr (4i+2-i^(2))/(4-i^(2)) = x +iy`
`rArr (4i-)/(4+1) = iy rArr (-2)/(5)+(4i)/(5) = x+iy`
On comparing both sides, we get
`x = 2//2 rArr y = 4/5`
`rArr" "x+y = (-2)/(5)+(4)/(5) = 2/5`
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