Question

How do you evaluate `e^( ( 19 pi)/12 i) - e^( ( pi)/4 i)` using trigonometric functions?

Answer 1

`e^((19pi)/12)-e^(pi/4)=-0.4483-i1.673`

Explanation:

`e^((19pi)/12i)=cos((19pi)/12)+isin((19pi)/12)` and `e^(pi/4i)=cos(pi/4)+isin(pi/4)`

Hence, `e^((19pi)/12)-e^(pi/4)=cos((19pi)/12)+isin((19pi)/12)-cos(pi/4)-isin(pi/4)`

= `cos((-5pi)/12)-cos(pi/4)+i(sin((-5pi)/12)-sin(pi/4))`

= `cos((5pi)/12)-1/sqrt2+i(-sin((5pi)/12)-1/sqrt2)`

= `0.2588-0.7071+i(-0.9659-0.7071)`

= `-0.4483-i1.673`