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 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 any complex number and |z-1| = |z+1| then show that |z| = y .

A complex number z with (Im)(z)=4 and a positive integer n be such that z/(z+n)=4i , then the value of n, is

A complex number z with (Im)(z)=4 and a positive integer n be such that z/(z+n)=4i , then the value of n, is

A complex number z with (Im)(z)=4 and a positive integer n be such that z/(z+n)=4i , then the value of n, 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 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.

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

A variable complex number z=x+iy is such that arg (z-1)/(z+1)= pi/2 . Show that x^2+y^2-1=0 .

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot