If `Z+alpha|Z-1|+2i=0`, then find the sum of maximum and minimum values of `alpha`.(`alpha in R`)

Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

If z=(1+i tan alpha)^(1+i) , then find the magnitude of Z.

If z^2+alphaz+beta has one root 1-2i , then find the value of alpha-beta (alpha,beta , in R)

For a complex number z,the minimum value of |z|+|z-cos alpha-i sin alpha| is

Find modulus and argument for z=1-sin alpha+i cos alpha,alpha in(0,2 pi)

If n>=3 and 1,alpha_(1),alpha_(2),alpha_(3)...alpha_(n-1) are the n, nth roots of unity then find the value of sum_(1<=i

If alpha=(z)/(bar(z)), then | alpha|

If alpha_(0),alpha_(1),alpha_(2)----alpha_(n-1) be the nth roots of unity then the value of sum_(r=0)^(n-1)(alpha_(r))/(3-alpha_(r)) is

If the function f(x)=x^(3)+alpha x^(2)+beta x+1 has maximum value at x=0 and minimum value at x=1, then (i)alpha=(2)/(3),beta=0 (ii) alpha=-(3)/(2),beta=0(iii)alpha=0,beta=(3)/(2)(iv) none of these