If `alpha = x + y + z + omega and beta = (xy + yz + zomega + omega x + omega y + xz)`, then which of the following statement(s), is/are true

Following are equations of four waves : (i) y_(1) = a sin omega ( t - (x)/(v)) (ii) y_(2) = a cos omega ( t + (x)/(v)) (iii) z_(1) = a sin omega ( t - (x)/(v)) (iv) z_(1) = a cos omega ( t + (x)/(v)) Which of the following statements are correct ?

Following are equations of four waves : (i) y_(1) = a sin omega ( t - (x)/(v)) (ii) y_(2) = a cos omega ( t + (x)/(v)) (iii) z_(1) = a sin omega ( t - (x)/(v)) (iv) z_(1) = a cos omega ( t + (x)/(v)) Which of the following statements are correct ?

Following are equations of four waves : (i) y_(1) = a sin omega ( t - (x)/(v)) (ii) y_(2) = a cos omega ( t + (x)/(v)) (iii) z_(1) = a sin omega ( t - (x)/(v)) (iv) z_(1) = a cos omega ( t + (x)/(v)) Which of the following statements are correct ?

Following are equations of four waves : (i) y_(1) = a sin omega ( t - (x)/(v)) (ii) y_(2) = a cos omega ( t + (x)/(v)) (iii) z_(1) = a sin omega ( t - (x)/(v)) (iv) z_(1) = a cos omega ( t + (x)/(v)) Which of the following statements are correct ?

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?

If x=a+b, y=a omega+b omega^(2), z=a omega^(2)+b omega , then x y z=