Question

Find the cube roots of 27(cos 279° + i sin 279°).

Answer 1

3 (cos 93 + i sin 93)

Explanation:

We are to find the cube roots of the following:

27 (cos 279° + i sin 279°)

`(cosx + i sin x) = cos (nx)) + i sin (nx)`

`27 * (cos 279+i sin 279)(1)/(3) =27(1)/(3) * (cos 279+i sin 279)(1)/(3)`

Simplifying this to get:

`3* (cos279+i sin279)(1)/(3)`

`3*(cos 279+i sin 279)13=3(cos (279)/(3) +i sin (279)/(3))`

We know that
`(279)/(3)=3`

So, cube root =
`3(cos 93 + i sin 93)`