If `n|q and A = {z in C:z^n = 1 },B{z:z^p=1}` then

If |z_(1)| = |z_(2)| = |z_(3)| = … |z_(n)| = 1 , then |z_(1) + z_(2) + z_(3) + ….. + z_(n) | =

If z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n in N , has the value

If z is a complex number satisfying z+z^(-1)=1 then z^(n)+z^(-n),n in N, has the value

If |z_(1)| = |z_(2)| = ….. |z_(n)| = 1 , prove that |z_(1) + z_(2) + …….. z_(n)| = |(1)/(z_(1)) + (1)/(z_(2)) + ……….. + (1)/(z_(n))| .

If a, b a n d c are in A.P., a x ,b y ,a n dc z in G.P. and x,y,z in H.P. then prove that x/z+z/x=a/c+c/a .

If z=x+iy is a complex number with x, y in Q and |z| = 1 , then show that |z^(2n)-1| is a rational numberfor every n in N .

If z=x+iy is a complex number with x, y in Q and |z| = 1 , then show that |z^(2n)-1| is a rational numberfor every n in N .