Question

How can you use trigonometric functions to simplify `9 e^( ( 7 pi)/4 i )` into a non-exponential complex number?

Answer 1

`9 e^((7 pi)/4 i) =6.363961- 6.363961 i`

Explanation:

`9 e^((7 pi)/4 i )`

We know `e^(i theta) = cos theta +i sin theta`

`theta= (7 pi)/4 ~~ 5.497787`

`:. 9 e^((7 pi)/4 i) = 9(cos ((7 pi)/4)+ i sin ((7 pi)/4))` or

`9 e^((7 pi)/4 i) =6.363961- 6.363961 i` [Ans]