Question

How do you evaluate `e^( ( 15 pi)/8 i) - e^( ( 13 pi)/12 i)` using trigonometric functions?

Answer 1

`1.89 - 0.064 i`

Explanation:

`(15pi)/8= (15*180)/8 = 337.5^0 ; (13pi)/12= (13*180)/12 = 195^0`

We know `e^(i theta) = cos theta + i sin theta :. e^((15pi)/8 i) = cos 337.5 + i sin 337.5 and e^((13pi)/12 i) = cos 195 + i sin 195`

`e^((15pi)/8 i) - e^((13pi)/12 i) = (cos 337.5 + i sin 337.5) - (cos 195 + i sin 195 ) = ( cos 337.5 - cos 195) +i ( sin 337.5 - sin 195) = (0.924 - (-0.966) + i (-0.383 - (-0.259) = 1.89 - 0.064 i`

`e^((15pi)/8 i) - e^((13pi)/12 i) = 1.89 - 0.124 i` [Ans]