1. For complex number z, the minimum value of |z| + |z – cosa – i sina|+|z – 2(cosa + i sina )| is...............

it can be written as:

|z| + |z-(e^ia)| + |z-2(e^ia)| 

we see.....oigin , e^ia , 2e^ia ,  forms a straight line.

and for minimum value..... z must coincide with e^ia

hence the equation becomes:

=|e^ia| + 0 + |-e^ia|

=1 + 0 + 1

=2(ANS)