Question

How do you evaluate `e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)` using trigonometric functions?

Answer 1

In complex terms, `R ( sintheta + i costheta )`= `Re ^ (i theta)`
where `R` is the modulus and `theta` is the argument.

So
`e^( ( 7 pi)/4 i) - e^( ( 19 pi)/12 i)` = `1 ( sin ( 7pi)/4 + i cos ( 7pi)/4 )`
- `1 ( sin ( 19 pi)/12 + i cos ( 19 pi)/12 )`

= `sin ( 7pi)/4 + i cos ( 7 pi)/4`
- `sin ( 19 pi)/12 + i cos ( 19 pi)/12`