If `z=x+iy (x, y in R, x !=-1/2)`, the number of values of z satisfying `|z|^n=z^2|z|^(n-2)+z |z|^(n-2)+1.` `(n in N, n>1)` is

If z=x+iy(x,y in R,x!=-(1)/(2)), the number of values of z satisfying |z|^(n)=z^(2)|z|^(n-2)+z|z|^(n-2)+1(n in N,n>1) is

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 be the complex numbers satisfying x^2 +4=2x, prove that z_1^n+z_2^n=2^(n+1) cosfrac(npi)(3) .

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

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 n is a natural number gt 2 , such that z^(n) = (z+1)^(n) , then

If z+1/z=2cos theta, prove that |(z^(2n)-1)/(z^(2n)+1)|=|tan n theta|