Question

How can you use trigonometric functions to simplify `4 e^( ( 11 pi)/6 i )` into a non-exponential complex number?

Answer 1

We get `-2\sqrt{3}+2i`.

Explanation:

Euler's formula `e^{ix}=cos x + i sin x` is the key. Here `x={11\pi}/6`, then:

`e^{i{11\pi}/6}=cos({11\pi}/6)+ i sin({11\pi}/6)`
`=-cos(\pi/6)+i sin(\pi/6)`
`({-\sqrt{3}}/2)+i(1/2)`

Multiplying by 4 then gives the answer.