Question

Find [4(cos15° + isin15°)]^3 and express it in a + bi form.

Answer 1

see explanation

Explanation:

Using De Moivre's theorem

Given

[ 4(cos15° + isin15° ) ]³, then

= 4³ [ cos(3 × 15°) + isin(3 × 15°) ]

= 64 (cos45° + isin45° )

= 64 (
`(√(2) )/(2)` +
`(√(2) )/(2)` i )

= 64 (
`(√(2) )/(2)` (1 + i) )

= 32
`√(2)` (1 + i)

= 32
`√(2)` + 32
`√(2)` i