For a complex number `z` the minimum value of `|z|+|z-cos alpha-i sin alpha|` (where `i=sqrt-1`) is:

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

z is a complex number. The minimum value of |z | + I z - 2| is

If z be a complex number, show that the minimum value of |z| + |z - 1| is 1.

If complex number z satisfies amp(z+i)=(pi)/(4) then minimum value of |z+1-i|+|z-2+3i| is

If the imaginary part of the complex number (z-1)(cos alpha-i sin alpha)+(z-1)^(-1)(cos alpha+i sin alpha) is zero,then which of the following options are correct? a) |z|=1 b) |z-1|=1 c) arg (z)=alpha d) arg (z-1)=alpha

If i^(2)=-1 , then for a complex number Z the minimum value of |Z|+|Z-3|+|Z+i|+|Z-3-2i| occurs at