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If alpha and beta are the complex roots ...

If `alpha` and `beta` are the complex roots of the equation `(1+i)x^(2)+(1-i)x-2i=0` where `i=sqrt(-1)`, the value of `|alpha-beta|^(2)` is

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The correct Answer is:
5
`:'(1+i)x^(2)+(1-i)x-2i=0`
`impliesx^(2)+((1-i))/((1+i))x-(2i)/((1+i))=0`
`impliesx^(2)-ix-(1+i)=0`
`:. alpha +beta=i` and `alpha beta =-(1+i)`
`:.alpha -beta=sqrt((alpha +beta)^(2)-4alpha beta)=sqrt(i^(2)+4(1+i))=sqrt((3+4i))`
`|alpha-beta|=sqrt(sqrt(9+16))=sqrt(5)`
`:.|alpha-beta|^(2)=5`
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