Evaluate: `lim_(z rarr1)(z^(1/3)-1)/(z^(1/6)-1)`

lim_(z to 1) (2^(1//3)-1)/(z^(1//6)-1)

lim_(x rarr0+)(xe^((1)/(x)))/(1+e^((1)/(z))))=

If z_(n)=cos((pi)/((2n+1)(2n+3)))+i sin((pi)/((2n+1)(2n+3))) ,then lim_(n rarr oo)(z_(1)*z_(2)*z_(3)...z_(n))=

If z^(2)+z+1=0 where z is a complex number, then the value of (z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+...+(z^(6)+(1)/(z^(6)))^(2) is

lim_(z rarr((2n+1)pi)/(2))[z-(2n+1)(pi)/(2)]xx(z)/(cos z)

If z^(2)+(1)/(z^(2))=14, find the value of z^(3)+(1)/(z^(3))

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 Then find the value of |z_(1)+z_(2)+z_(3)| is :

If z_(1),z_(2),z_(3) are complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 Then find the value of |z_(1)+z_(2)+z_(3)| is :