If `z + z^(-1)= 1`, then find the value of `z^(100) + z^(-100)`.

If |z+1|=z+2(1+i) then find the value of z.

if |z|=1, then find the value of (1+z)/(1-z) .

If sin^(-1) x +sin^(-1)y +sin^(-1) z =(3pi)/(2) , then find the value of x^(100) +y^(100) +z^(100) -(9)/(x^(101)+y^(101)+z^(101)) .

If sin ^(-1) x + sin ^(-1) y + sin ^(-1) z = (3pi)/(2) then the value of x ^(100) + y ^(100) + z ^(100) - (3)/( x ^(101) + y^(101) + z ^(101)) is

If |z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)+ z_(2)z_(3)|= 12 , then find the value of |z_(1) + z_(2) + z_(3)| .

If |z_(1)| = 1, |z_(2)| =2, |z_(3)|=3, and |9z_(1)z_(2) + 4z_(1)z_(3)+z_(2)z_(3)|= 12 , then find the value of |z_(1) + z_(2) + z_(3)| .

If (z-1)/(z+1) is a purely imaginary number (z ne - 1) , then find the value of |z| .

If (z-1)/(z+1) is a purely imaginary number (z ne - 1) , then find the value of |z| .

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))