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 is a complex number satisfying the relation ∣z+1∣=z+2(1+i) then z is

If z is a complex number such that |z|>=2 then the minimum value of |z+1/2| is

lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imaginary, then |z| is equal to

If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)=(pi)/(2) then show that barzw=-i

If z=x+iy , where x and y are real numbers and |x|+|y| lt= k|z| then k=.....

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

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

If z_1a n dz_2 are two complex numbers and c >0 , then prove that |z_1+z_2|^2lt=(1+c)|z_1|^2+(1+c^(-1))|z_2|^2dot

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]

Let z=x+i y be a complex number where x and y are integers. Then, the area of the rectangle whose vertices are the roots of the equation z bar(z)^3+ bar(z) z^3=350 is