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

If sin^(-1)x+sin^(-1) y + sin ^(-1) z = (3pi)/2 , the value of x^(100)+y^(100)+z^(100) -9/(x^(101)+y^(101)+z^(101)) is : (i)0 (ii)1 (iii)2 (iv)3

Let i= sqrt-1 . If a sequence of complex numbers is defined by z_(1)=0, z_(n+1)= z_(n)^(2)+i for n ge 1 , then find the value of z_(111) .

If (-1)ltx, y, z le 1 such that sin ^(-1) x+sin ^(-1) y+sin ^(-1) z=(3 pi)/2 , find the value of x^(2000)+y^(2001)+z^(2002)-(9/(x^(2000)+y^(2001)+z^(2002)))

If z+ sqrt2 |z+1| +ii=0 then the value of |z|^(2) is

If z=1+i , then the argument of z^(2)e^(z-i) is

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

If (pi)/(3) and (pi)/(4) are argument of z_(1) and bar(z)_(2) then the value of arg (z_(1)z_(2)) is

If z= r (cos theta + i sin theta) , then the value of (z)/(bar(z)) + (bar(z))/(z) is

If z is a complex number such that z+ |z|=8 +12i then the value of |z^2| is

If |z|=1 and z ne +- 1 , then one of the possible values of arg(z)- arg (z+1)- arg (z-1) , is