Show that : `sum_(r=0)^(n-1)|z_1+alpha^r z_2|^2=n(|z_1|^2+|z_2 |^2)` where `alpha : r=0,1,2....(n-1),` are the nth roots of unity and `z_1,z_2` are any two complex numbers.

Show that: sum_(r=0)^(n-1)|z_1+alpha^r z_2|^2=n(|z_1|^2+|z_2|^2),w h e r e, alpha ; r=0,1,2,...,(n-1) , are the nth roots of unity and z_1, z_2 are any two complex numbers.

Show that: sum_(r=0)^(n-1)|z_1+alpha^r z_2|^2=n(|z_1|^2+|z_2|^2),w h e r e, alpha ; r=0,1,2,...,(n-1) , are the nth roots of unity and z_1, z_2 are any two complex numbers.

Show that: sum_(r=0)^(n-1)|z_1+alpha^r z_2|^2=n(|z_1|^2+|z_2|^2),w h e r ealpha^r ; r=0,1,2, ,(n-1) , are nth roots of unity and z_1, z_2 are an tow complex numbers.

1,z_(1),z_(2),z_(3),......,z_(n-1), are the nth roots of unity, then (1-z_(1))(1-z_(2))...(1-z_(n-1)) is

If 1,z_1z_2,……z_(n-1) are the n^th roots of unity, then (1-z_1)(1-z_2)…..(1-z_(n-1))= .

If z_(1) and z_(2) are two n^(th) roots of unity, then arg (z_(1)/z_(2)) is a multiple of

If z_(1) and z_(2) are two n^(th) roots of unity, then arg (z_(1)/z_(2)) is a multiple of

If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unity and z_(1) and z_(2) are any two complex numbers such that sum_(r=0)^(n-1)|z_(1)+alpha^(R ) z_(2)|^(2)=lambda(|z_(1)|^(2)+|z_(2)|^(2)) , then lambda=

If 1,alpha,alpha^(2),………..,alpha^(n-1) are the n, n^(th) roots of unity and z_(1) and z_(2) are any two complex numbers such that sum_(r=0)^(n-1)|z_(1)+alpha^(R ) z_(2)|^(2)=lambda(|z_(1)|^(2)+|z_(2)|^(2)) , then lambda=

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n