If a=`frac{-1+sqrt3 i}{2}`, b=`frac{-1-sqrt3 i}{2}`, then show that `a^2`=b and `b^2`=a

If z= frac{sqrt3+i}{2} , then z^69

Solve the following: If a = (-1 + sqrt(3)i) / 2 , b = (-1 - sqrt(3)i) / 2 , show that a^2 = b and b ^2 = a

If z = frac{sqrt 3 + i}{2} , then z^69 =

[frac{sqrt3+i}{2}]^6+[frac{i-sqrt3}{2}]^6 is equal to

If a+ib= frac{1+i}{1-i} , then prove that ( a^2 + b^2 )=1

Value of [frac{-1+sqrt(-3)}{2}]^40 +[frac{-1-sqrt(-3)}{2}]^40 is

If x+frac{1}{x}= sqrt3 , then x=

If z=[frac{sqrt3}{2}+frac{i}{2}]^5+[frac{sqrt3}{2}-frac{i}{2}]^5 , then

[frac{1+i}{sqrt2}]^8+[frac{1-i}{sqrt2}]^8

If z= frac{-2}{1+sqrt3i} , then the value of arg(z) is