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

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) class=

Answer :

Moivre's theorem says

[tex]\lbrack r(\cos \theta+i\sin \theta)\rbrack^n=r^n(\cos n\theta+i\sin n\theta)[/tex]

in our case

[tex](\cos (\frac{3\pi}{5})+i\sin (\frac{3\pi}{5}))^3[/tex]

r=1

[tex](\cos (\frac{3\cdot3\pi}{5})+i\sin (\frac{3\cdot3\pi}{5}))[/tex][tex](\cos (\frac{9\pi}{5})+i\sin (\frac{9\pi}{5}))[/tex]

ANSWER

[tex]C.(\cos (\frac{9\pi}{5})+i\sin (\frac{9\pi}{5}))[/tex]

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