[" EXAMPLE "42" The number of roots of the equation "z^(15)=1" satisfying "],[|arg(z)|

The number of roots of the equation z^15=1 satisfying abs(argz)ltpi/2 are

Find the number of roots of the equation z^(15) = 1 satisfying |arg z| lt pi//2 .

Find the number of roots of the equation z^(15) = 1 satisfying |arg z| lt pi//2 .

The complex number z satisfying the equation |z-i|=|z+1|=1 is

The complex number z satisfying the equation |z-i|=|z+1|=1

If z_(1),z_(2),z_(3) are any three roots of the equation z^(6)=(z+1)^(6), then arg((z_(1)-z_(3))/(z_(2)-z_(3))) can be equal to

If z_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

If z_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

Let two distinct complex numbers z_1 and z_2 both satisfy the equation z+ bar(z) = 2 |z-1| and "arg" (z_1 -z_2)=(pi)/(4) , then

The number of values of z satisfying both theequations Arg(z-1-i)=-(3 pi)/(4) and Arg(z-2-2i)=(pi)/(4) is