Find the real values of x and y for which :
`{:((i),(1-i)x+(1+i)y=1 - 3i,(ii),(x+iy)(3-2i)=(12+5i)),((iii),x+4yi =ix + y + 3,(iv),(1+i)y^(2)+(6+i)=(2+i)x),((v),((x+3i))/((2+iy))=(1-i),(vi),((1+i)x-2i)/((3+i))+((2-3i)y+i)/((3-i))=i):}`

Answer

`{:((i),"x = 2, y = -1",(ii),"x =2, y = 3",(iii),"x = 4, y = 1"),((iv),(x=5","y=2)or(x=5","y= -2),(v),x=7","y=5,(vi),x=3","y = -1):}`

Explanation

(iv) `(y^(2)+6-2x)+(y^(2)-x+1)i=0 rArr y^(2) + 6 - 2x = 0, y^(2) - x + 1 = 0`
`rArr" "y^(2) -2x = -6 and y^(2) - x = -1`.
On subtracting, we get x = 5.
`therefore" "y^(2)-5 = -1 rArr y^(2) = 4 rArr y = +- 2`.
(v) `(x+3i) = (1-i) (2 + iy)`
`rArr" "(x+3i)=(2+y)+(y-2)i rArr (x-y-2) + i(5-y)=0`
`rArr" "x-y-2=0 and 5 - y = 0`.
(vi) `{x+(x-2)i} (3-i)+{2y+(1-3y)i} (2+i) = i(3+i)(3-i)`
`rArr" "{3x+(x-2)}+{3(x-2)-x}i + {6y - (1-3y)} + {2y+(3-9y}i = 10i`
`rArr" "(4x-2+9y-1)+(2x-6+3-7y)i = 10i`
`rArr" "(4x + 9y - 3)+(2x-7y-3)i = 10i`
rArr" "4x + 9y = 3 and 2x - 7y = 13`.