Mathematics, 22.09.2019 10:50 12camtheman
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
Answers: 1
![\large {\boxed {[r( \cos \theta + i\sin \theta)]^n = r^n(\cos n\theta + i\sin n\theta)} }](/tpl/images/0251/9108/84082.png)
![[\cos (\frac{3 \pi}{12}) + i\sin (\frac{3 \pi}{12})]^5 = \cos (5 \times \frac{3 \pi}{12}) + i\sin (5 \times \frac{3 \pi}{12})](/tpl/images/0251/9108/f0395.png)
![\large {\boxed {[\cos (\frac{3 \pi}{12}) + i\sin (\frac{3 \pi}{12})]^5 = \cos (\frac{15 \pi}{12}) + i\sin (\frac{15 \pi}{12})}}](/tpl/images/0251/9108/9bdc4.png)
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Use de moivre's theorem to write the complex number in trigonometric form: (cos(3pi/12) + i sin (3p...
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