निम्नलिखित में x और y के मान ज्ञात कीजिए-
(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)`

Explanation

(i) `x+3i=6-9iy`
`implies x=6` और `3=-9y`
`implies x=6` और `y=-1/3`
(ii) `(x+iy)-(3-2i)=5+i`
`implies x+iy=(5+i)+(3-2i)=8-i`
`implies x=8` और `y=-1`
(iii) `i=x+2yi`
`implies 0+1.i=x+2yi`
`implies x=0` और `2y=1`
`implies x=0` और `y=1/2`
(iv) `4x+i(x-y)=2-5i`
`implies 4x=2` और `x-y=-5`
`4x=2 implies x=1/2`
और `x-y=-5`
`implies 1/2 -y=-5`
`implies y=11/2`
`:. x=1/2` और `y=11/2`
(v) `(x+2iy)(2-i)^(2)=10(1-i)`
`implies 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)))/(-16i^(2))`
`=(10(7+i))/25 =14/5+2/5 i`
`implies x=14/5` और `2y=2/5`
`implies x=14/5` और `y=1/5`