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Let (-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=s...

Let `(-2-(1)/(3)i)^(3) = (x+iy)/(27) (i=sqrt(-1))`, where x and y are real numbers. Then y - x equals

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The correct Answer is:
B
We have `(x+iy)/(27)(-2 - 1/3 i)^3=[-1/3 (6+i)]^3`
`rArr (x+iy)/(27)=-1/27(216+108 i+ 18 i^2+i^3)`
`=-1/27(198+107 i)`
`[ therefore (a+b)^3=a^3+b^3+3a^2b + 3ab^2,i^2=-1,i^3=-1]`
On equating real and imaginary part , we get
`x=- 198 and y = - 107`
`rArr y-x= -107 + 198 = 91 `
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