Question

Use De Moivre's theorem to write the complex number in trigonometric form. BT + sih 37 5 A. 3 cos 37T BET O A :(+(2) . (7) om Can | --| ) Oc(+1). -(0) OD(). (7) 977 97 1 Ос COS + 92T D. 3 cos + isin IT 6

Answer 1

Moivre's theorem says

`\lbrack r(\cos \theta+i\sin \theta)\rbrack^n=r^n(\cos n\theta+i\sin n\theta)`

in our case

`(\cos ((3\pi)/(5))+i\sin ((3\pi)/(5)))^3`

r=1

`(\cos ((3\cdot3\pi)/(5))+i\sin ((3\cdot3\pi)/(5)))`
`(\cos ((9\pi)/(5))+i\sin ((9\pi)/(5)))`

ANSWER

`C.(\cos ((9\pi)/(5))+i\sin ((9\pi)/(5)))`