The value of `sin[log_e{(cos(pi/2)+isin(pi/2)}^z]` is, where `z` satisfies the equation `|z-2i|=1`and has least modulus

The value of sin [log_(e){((cos pi)/(2)+i(sin pi)/(2))^(z)}] is where z satisfies the equation |z-2i|=1 and has the last modulus

z=cos(pi/6)+isin(pi/6)=?

z=(1-i)/(cos(pi/3)+i sin(pi/3))

locus of the point z satisfying the equation |z-1|+|z-i|=2 is

If z = cos"" pi/4+ isin (pi/6) ,then

The number of values of x in[0,n pi],n in Z that satisfy the equation log_(|sin x|)(1+cos x)=2 is

2.The value of x satisfying the equation log_(cos x)sin x=1 , where 0< x < (pi)/2 is

If z_r=cos(pi/3^r)+i sin(pi/3^r) where r in N then z_1.z_2.z_3...oo=

Complex numbers z satisfy the equaiton |z-(4//z)|=2 The value of arg(z_(1)//z_(2)) where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, can be