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For any complex number w=c+id let arg(w)...

For any complex number `w=c+id` let `arg(w) in (-pi,pi] , where i =sqrt(-1)`. Let `alpha and beta` be real number such that all complex number `z=x+iy` satisfying `arg((z+alpha)/(z+beta))=pi/4` , the ordered pair (x,y) lies on the circle `(x^2+y^2+5x-3y+4=0)`
Then which of the following statement is(are) TRUE?

A

`alpha=-1`

B

`alpha.beta=4`

C

`alpha.beta=-4`

D

`beta=4`

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