Question

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

Answer 1

Given the complex number:

`(\cos ((3\pi)/(12))+i\sin ((3\pi)/(12)))^5`

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

so,

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

Apply the rule, so the number will be:

`\cos ((15\pi)/(12))+i\sin ((15\pi)/(12))`

so, the answer will be option D