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`

The complex number z = x + iy , which satisfies the equation |(z-5i)/(z+5i)| =1 , lies on:

If z_1, z_2 are two complex numbers satisfying the equation |(z_1 +z_2)/(z_1 -z_2)|=1 , then z_1/z_2 is a number which is :

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

If two complex numbers z_1,z_2 are such that |z_1|= |z_2| , is it then necessary that z_1 = z_2 ?

If the complex number z_1 and z_2 be such that arg(z_1)-arg(z_2)=0 , then show that |z_1-z_2|=|z_1|-|z_2| .

It is known that x+y=10 and that x=z. show that z+y=10?

If z=x+iy and |z|=1, show that the complex number z_1=(z-1)/(z+1) is purely imagine.

If z_1a n dz_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to

If x,y and z are three real numbers such that x+y+z=4 and x^2+y^2+z^2=6 ,then show that each of x,y and z lie in the closed interval [2/3,2]

If z=x+i ya n dx^2+y^2=16 , then the range of ||x|-|y|| is