Find the values of `x and y`: (i) `x+3i=6-9iy` (ii) `(x+iy)-(3-2i)=5+i` (iii) `i=x+2yi` (iv) `4x+i(x-y)=2-5i` (v) `(x+2iy)(2-i)^(2)=10(1-i)`

Answer

N/a

Explanation

(i) `x+3i=6-9iy`
`rArr" "x=6 and 3=-9y`
`rArr" "x=6 and y= -(1)/(3)`.
(ii) `(x+iy)-(3-2i)=5+i`
`rArr" "x+iy=(5+i)+(3-2i)`
`rArr" "x=8 and y=-1 `.
(iii) `" "i=x+2yi`
`rArr" "0+1*i=x+2yi`
`rArr" "x = 0 and 2y= 1 `
`rArr" "x=0 and y= (1)/(2)`.
(iv) `" "4x+i(x-y)=2-5i`
`rArr" "4x=2 and x-y=-5`
`" "4x=2 rArr x=(1)/(2)`
and `" "x-y=-5`
`rArr" "(1)/(2)-y=-5`
`rArr" "y=(11)/(2)`
`therefore" "x=(1)/(2) and y=(11)/(2)`.
(v) `" "(x+2iy)(2-i)^(2)=10(1-i)`
`rArr" "x+2iy=(10(1-i))/((2-i)^(2))=(10(1-i))/(4+i^(2)-4i)`
`" "=(10(1-i))/(3-4i)=(10(1-i))/(3-4i)xx(3+4i)/(3+4i)`
`" "=(10(3+4i-3i-4i^(2)))/(9-16i^(2))`
`" "=(10(7+i))/(25)=(14)/(5)+(2)/(5)i`
`rArr" "x=(14)/(5) and 2y=(2)/(5)`
`rArr" "x=(14)/(5) and y=(1)/(5)`.