If `z+1/z=2cos6^@` , then `z^1000+1/[z^1000]` +1 is equal to

If z=(1)/(z)=2 cos 60^(@) , then z^(1000)+(1)/(z^(1000))+1 is equal to

z is a complex number such that z+1/z=2cos 3^0 ,then the value of z^(2000)+ 1/z^(2000) is equal to

Z is a complex number such that z+(1)/(z)=2cos3^(0), then the value of z^(2000)+(1)/(z^(2000)) is equal to

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then z 1 ​ +z 2 ​ is equal to

If z 1 ​ and z 2 ​ are two non zero complex numbers such that ∣z 1 ​ +z 2 ​ ∣=∣z 1 ​ ∣+∣z 2 ​ ∣ then arg z 1 ​ -arg z 2 ​ is equal to

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to

If for the complex numbers z_1 and z_2 , |z_1+z_2|=|z_1-z_2| , then Arg(z_1)-Arg(z_2) is equal to