e^((7pi i)/6)= cos ((7pi)/6) + i sin ((7pi)/6)e7πi6=cos(7π6)+isin(7π6)
= -cos pi/6 - i sin pi/6−cosπ6−isinπ6 [(7pi)/6 = pi +pi/6[7π6=π+π6, In the third quadrant both sin and cos would b negative]
Like wise e^((14pi i)/3)= cos ((14pi)/3) + i sin ((14pi)/3)e14πi3=cos(14π3)+isin(14π3)
= cos ((2pi)/3) + i sin ((2pi)/3)cos(2π3)+isin(2π3) [(14pi)/3= 4pi +(2pi)/3= (2pi)/3][14π3=4π+2π3=2π3]
= - cos (pi/3) +i sin (pi/3) −cos(π3)+isin(π3)
Now combining both expressions, it would be -sqrt3 /2 -i/2 +1/2 -i sqrt3 /2−√32−i2+12−i√32