How do you evaluate e^( ( pi)/4 i) - e^( ( 7 pi)/6 i) using trigonometric functions?

1 Answer
Jan 9, 2018

e^((pi i)/4) = cos (pi/4) + i sin (pi/4)= (sqrt2)/2 +i(sqrt2)/2

e^((7pi i)/6)= cos (7pi/6)+ isin (7pi/6)= -cos (pi/6)-isin (pi/6)
=-sqrt3/2 -i1/2
(In the third quadrant both sin and cos are negative)

Thus, e^((pi i)/4) -e^((7pi i)/6)= (sqrt2 +sqrt3)/2 +i(sqrt2 +1)/2