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Use De Moivre's theorem to write the complex number in trigonometric form, 3 Зл COS + i sin 12 12 O A. 5(cos(8)+isin() ( 5 Зя COS 12 137 12 31 O B. cos +isin Зл 60 60 5 C. cos COS 35 12 + i sin 3л 12 151 O D. cos + i sin 15л 12 12

Use De Moivres theorem to write the complex number in trigonometric form 3 Зл COS i sin 12 12 O A 5cos8isin 5 Зя COS 12 137 12 31 O B cos isin Зл 60 60 5 C cos class=

Respuesta :

Given the complex number:

[tex](\cos (\frac{3\pi}{12})+i\sin (\frac{3\pi}{12}))^5[/tex]

We will use De Moivre's theorem to write the complex number in trigonometric form.

so,

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

Apply the rule, so the number will be:

[tex]\cos (\frac{15\pi}{12})+i\sin (\frac{15\pi}{12})[/tex]

so, the answer will be option D

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