Question

Use De Moivre's theorem to write the complex number in trigonometric form:
(cos(3pi/12) + i sin (3pi/12))^5

A) cos(15 pi/12) + isin (15pi/12)
B) 5(cos(3 pi/12) + isin (3 pi/12)
C) Cos (3pi/60) + isin (3pi/60)
D) Cos (3pi/12)^5+i sin (3pi/12)^5

Answer 1

What is De Moivre's theorem?

Answer 2

De Moivre's Theorem let's us deal with the exponent on the outside:
\[\Large\rm \left[\cos\left(\color{orangered}{\theta}\right)+\mathcal i \sin\left(\color{orangered}{\theta}\right)\right]^c=\left[\cos\left(\color{orangered}{c\theta}\right)+\mathcal i \sin\left(\color{orangered}{c\theta}\right)\right]\]So just bring it inside as a coefficient multiplying your angle.

Answer 3

I feel like in that case it'd be either C or D, right?!

Answer 4

\[\large\rm \left[\cos\left(\color{orangered}{\frac{3\pi}{12}}\right)+\mathcal i \sin\left(\color{orangered}{\frac{3\pi}{12}}\right)\right]^5=\left[\cos\left(\color{orangered}{5\cdot\frac{3\pi}{12}}\right)+\mathcal i \sin\left(\color{orangered}{5\cdot\frac{3\pi}{12}}\right)\right]\]

Answer 5

Remember how to multiply a whole number by a fraction?
Just bring it up into the numerator.

Answer 6

got it! so in that case it'd be A, right?!

Answer 7

Mmmm yes, good job c:

Answer 8

thank you for your help!!!