Answer:
Option B
Explanation:
Here , S=S1∩S2∩S3
S1={z∈C:|z|<4}
∴ S1 :x2+y2 < 4 ...........(i)
and S2 ={z∈C:In[z−1+√3i1−√3i]>0}
where z−1+i√31−i√3=(x−1)+i(y+√3)1−i√3
= (x−1)(1+i√3)+i(y+√3)(1+i√3)1+3
=(x−1)+i√3(x−1)+i(y+√3)−√3(y+√3)4
=(x−1−√3y−3)4+i(√3x+y)4
∴ s2:√3x+y>0 .......(ii)
S3={z∈C:Rez>0}
s3:x>0 ......(iii)
s3:x>0 ......(iii)
Since ,
S=S1∩S2∩S3

Clearly , the shaded region represents the area of sector
∴ S=12r2θ=12×42×5π6=20π3