Question

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

Answer 1

Correct Answer - 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 `