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+i y is a complex number with x ,y in Qa n d|z|=1, then show that |z^(2n)-1| is a rational number for every n in Ndot

If z = x+iy is any complex number and |z-1| = |z+1| then show that |z| = y .

If z=x+iy is any complex number and |z-1|=|z+1| then show that |z|=y

If z is a complex number with |z|=1 and z+(1)/(z)=x+iy , then xy=

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

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 complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

If z_1 is a complex number other than -1 such that |z_1|=1\ a n d\ z_2=(z_1-1)/(z_1+1) , then show that the real parts of z_2 is zero.